glibc/sysdeps/ieee754/dbl-64/e_log.c

/* Double-precision log(x) function.
   Copyright (C) 2018-2020 Free Software Foundation, Inc.
   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, see
   <https://www.gnu.org/licenses/>.  */

#include <math.h>
#include <stdint.h>
#include <math-svid-compat.h>
#include <shlib-compat.h>
#include <libm-alias-double.h>
#include "math_config.h"

#define T __log_data.tab
#define T2 __log_data.tab2
#define B __log_data.poly1
#define A __log_data.poly
#define Ln2hi __log_data.ln2hi
#define Ln2lo __log_data.ln2lo
#define N (1 << LOG_TABLE_BITS)
#define OFF 0x3fe6000000000000

/* Top 16 bits of a double.  */
static inline uint32_t
top16 (double x)
{
  return asuint64 (x) >> 48;
}

#ifndef SECTION
# define SECTION
#endif

double
SECTION
__log (double x)
{
  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  double_t w, z, r, r2, r3, y, invc, logc, kd, hi, lo;
  uint64_t ix, iz, tmp;
  uint32_t top;
  int k, i;

  ix = asuint64 (x);
  top = top16 (x);

#define LO asuint64 (1.0 - 0x1p-4)
#define HI asuint64 (1.0 + 0x1.09p-4)
  if (__glibc_unlikely (ix - LO < HI - LO))
    {
      /* Handle close to 1.0 inputs separately.  */
      /* Fix sign of zero with downward rounding when x==1.  */
      if (WANT_ROUNDING && __glibc_unlikely (ix == asuint64 (1.0)))
	return 0;
      r = x - 1.0;
      r2 = r * r;
      r3 = r * r2;
      y = r3 * (B[1] + r * B[2] + r2 * B[3]
		+ r3 * (B[4] + r * B[5] + r2 * B[6]
			+ r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10])));
      /* Worst-case error is around 0.507 ULP.  */
      w = r * 0x1p27;
      double_t rhi = r + w - w;
      double_t rlo = r - rhi;
      w = rhi * rhi * B[0]; /* B[0] == -0.5.  */
      hi = r + w;
      lo = r - hi + w;
      lo += B[0] * rlo * (rhi + r);
      y += lo;
      y += hi;
      return y;
    }
  if (__glibc_unlikely (top - 0x0010 >= 0x7ff0 - 0x0010))
    {
      /* x < 0x1p-1022 or inf or nan.  */
      if (ix * 2 == 0)
	return __math_divzero (1);
      if (ix == asuint64 (INFINITY)) /* log(inf) == inf.  */
	return x;
      if ((top & 0x8000) || (top & 0x7ff0) == 0x7ff0)
	return __math_invalid (x);
      /* x is subnormal, normalize it.  */
      ix = asuint64 (x * 0x1p52);
      ix -= 52ULL << 52;
    }

  /* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
     The range is split into N subintervals.
     The ith subinterval contains z and c is near its center.  */
  tmp = ix - OFF;
  i = (tmp >> (52 - LOG_TABLE_BITS)) % N;
  k = (int64_t) tmp >> 52; /* arithmetic shift */
  iz = ix - (tmp & 0xfffULL << 52);
  invc = T[i].invc;
  logc = T[i].logc;
  z = asdouble (iz);

  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2.  */
  /* r ~= z/c - 1, |r| < 1/(2*N).  */
#ifdef __FP_FAST_FMA
  /* rounding error: 0x1p-55/N.  */
  r = __builtin_fma (z, invc, -1.0);
#else
  /* rounding error: 0x1p-55/N + 0x1p-66.  */
  r = (z - T2[i].chi - T2[i].clo) * invc;
#endif
  kd = (double_t) k;

  /* hi + lo = r + log(c) + k*Ln2.  */
  w = kd * Ln2hi + logc;
  hi = w + r;
  lo = w - hi + r + kd * Ln2lo;

  /* log(x) = lo + (log1p(r) - r) + hi.  */
  r2 = r * r; /* rounding error: 0x1p-54/N^2.  */
  /* Worst case error if |y| > 0x1p-4: 0.519 ULP (0.520 ULP without fma).
     0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma).  */
  y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi;
  return y;
}
#ifndef __log
strong_alias (__log, __ieee754_log)
strong_alias (__log, __log_finite)
# if LIBM_SVID_COMPAT
versioned_symbol (libm, __log, log, GLIBC_2_29);
libm_alias_double_other (__log, log)
# else
libm_alias_double (__log, log)
# endif
#endif