sysdeps/ieee754/flt-32/e_logf.c

   1 /* Single-precision log 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 "math_config.h"
  23
  24 /*
  25 LOGF_TABLE_BITS = 4
  26 LOGF_POLY_ORDER = 4
  27
  28 ULP error: 0.818 (nearest rounding.)
  29 Relative error: 1.957 * 2^-26 (before rounding.)
  30 */
  31
  32 #define T __logf_data.tab
  33 #define A __logf_data.poly
  34 #define Ln2 __logf_data.ln2
  35 #define N (1 << LOGF_TABLE_BITS)
  36 #define OFF 0x3f330000
  37
  38 float
  39 __logf (float x)
  40 {
  41   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  42   double_t z, r, r2, y, y0, invc, logc;
  43   uint32_t ix, iz, 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) /* log(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 - LOGF_TABLE_BITS)) % N;
  71   k = (int32_t) tmp >> 23; /* arithmetic shift */
  72   iz = ix - (tmp & 0x1ff << 23);
  73   invc = T[i].invc;
  74   logc = T[i].logc;
  75   z = (double_t) asfloat (iz);
  76
  77   /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
  78   r = z * invc - 1;
  79   y0 = logc + (double_t) k * Ln2;
  80
  81   /* Pipelined polynomial evaluation to approximate log1p(r).  */
  82   r2 = r * r;
  83   y = A[1] * r + A[2];
  84   y = A[0] * r2 + y;
  85   y = y * r2 + (y0 + r);
  86   return (float) y;
  87 }
  88 #ifndef __logf
  89 strong_alias (__logf, __ieee754_logf)
  90 strong_alias (__logf, __logf_finite)
  91 versioned_symbol (libm, __logf, logf, GLIBC_2_27);
  92 #endif