math/logf.c

/*
 * Single-precision log function.
 *
 * Copyright (c) 2017, Arm Limited.
 * SPDX-License-Identifier: Apache-2.0
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

#if WANT_SINGLEPREC
#include "single/e_logf.c"
#else

#include <math.h>
#include <stdint.h>
#include "math_config.h"

/*
LOGF_TABLE_BITS = 4
LOGF_POLY_ORDER = 4

ULP error: 0.818 (nearest rounding.)
Relative error: 1.957 * 2^-26 (before rounding.)
*/

#define T __logf_data.tab
#define A __logf_data.poly
#define Ln2 __logf_data.ln2
#define N (1 << LOGF_TABLE_BITS)
#define OFF 0x3f330000

float
logf (float x)
{
  /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  double_t z, r, r2, y, y0, invc, logc;
  uint32_t ix, iz, tmp;
  int k, i;

  ix = asuint (x);
#if WANT_ROUNDING
  /* Fix sign of zero with downward rounding when x==1.  */
  if (unlikely (ix == 0x3f800000))
    return 0;
#endif
  if (unlikely (ix - 0x00800000 >= 0x7f800000 - 0x00800000))
    {
      /* x < 0x1p-126 or inf or nan.  */
      if (ix * 2 == 0)
	return __math_divzerof (1);
      if (ix == 0x7f800000) /* log(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 - LOGF_TABLE_BITS)) % N;
  k = (int32_t) tmp >> 23; /* arithmetic shift */
  iz = ix - (tmp & 0x1ff << 23);
  invc = T[i].invc;
  logc = T[i].logc;
  z = (double_t) asfloat (iz);

  /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
  r = z * invc - 1;
  y0 = logc + (double_t) k * Ln2;

  /* Pipelined polynomial evaluation to approximate log1p(r).  */
  r2 = r * r;
  y = A[1] * r + A[2];
  y = A[0] * r2 + y;
  y = y * r2 + (y0 + r);
  return (float) y;
}
#endif