/* Single-precision log2 function.

   Copyright (C) 2017-2018 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

   <http://www.gnu.org/licenses/>.  */

#include <math.h>

#include <stdint.h>

#include <shlib-compat.h>

#include <libm-alias-float.h>

#include "math_config.h"

/*

LOG2F_TABLE_BITS = 4

LOG2F_POLY_ORDER = 4

ULP error: 0.752 (nearest rounding.)

Relative error: 1.9 * 2^-26 (before rounding.)

*/

#define N (1 << LOG2F_TABLE_BITS)

#define T __log2f_data.tab

#define A __log2f_data.poly

#define OFF 0x3f330000

float

__log2f (float x)

{

  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */

  double_t z, r, r2, p, y, y0, invc, logc;

  uint32_t ix, iz, top, tmp;

  int k, i;

  ix = asuint (x);

#if WANT_ROUNDING

  /* Fix sign of zero with downward rounding when x==1.  */

  if (__glibc_unlikely (ix == 0x3f800000))

    return 0;

#endif

  if (__glibc_unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))

    {

      /* x < 0x1p-126 or inf or nan.  */

      if (ix * 2 == 0)

	return __math_divzerof (1);

      if (ix == 0x7f800000) /* log2(inf) == inf.  */

	return x;

      if ((ix & 0x80000000) || ix * 2 >= 0xff000000)

	return __math_invalidf (x);

      /* x is subnormal, normalize it.  */

      ix = asuint (x * 0x1p23f);

      ix -= 23 << 23;

    }

  /* 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 >> (23 - LOG2F_TABLE_BITS)) % N;

  top = tmp & 0xff800000;

  iz = ix - top;

  k = (int32_t) tmp >> 23; /* arithmetic shift */

  invc = T[i].invc;

  logc = T[i].logc;

  z = (double_t) asfloat (iz);

  /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */

  r = z * invc - 1;

  y0 = logc + (double_t) k;

  /* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */

  r2 = r * r;

  y = A[1] * r + A[2];

  y = A[0] * r2 + y;

  p = A[3] * r + y0;

  y = y * r2 + p;

  return (float) y;

}

#ifndef __log2f

strong_alias (__log2f, __ieee754_log2f)

strong_alias (__log2f, __log2f_finite)

versioned_symbol (libm, __log2f, log2f, GLIBC_2_27);

libm_alias_float_other (__log2, log2)

#endif