logf.c raw

   1  /*
   2   * Single-precision log function.
   3   *
   4   * Copyright (c) 2017-2018, Arm Limited.
   5   * SPDX-License-Identifier: MIT
   6   */
   7  
   8  #include <math.h>
   9  #include <stdint.h>
  10  #include "libm.h"
  11  #include "logf_data.h"
  12  
  13  /*
  14  LOGF_TABLE_BITS = 4
  15  LOGF_POLY_ORDER = 4
  16  
  17  ULP error: 0.818 (nearest rounding.)
  18  Relative error: 1.957 * 2^-26 (before rounding.)
  19  */
  20  
  21  #define T __logf_data.tab
  22  #define A __logf_data.poly
  23  #define Ln2 __logf_data.ln2
  24  #define N (1 << LOGF_TABLE_BITS)
  25  #define OFF 0x3f330000
  26  
  27  float logf(float x)
  28  {
  29  	double_t z, r, r2, y, y0, invc, logc;
  30  	uint32_t ix, iz, tmp;
  31  	int k, i;
  32  
  33  	ix = asuint(x);
  34  	/* Fix sign of zero with downward rounding when x==1.  */
  35  	if (WANT_ROUNDING && predict_false(ix == 0x3f800000))
  36  		return 0;
  37  	if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000)) {
  38  		/* x < 0x1p-126 or inf or nan.  */
  39  		if (ix * 2 == 0)
  40  			return __math_divzerof(1);
  41  		if (ix == 0x7f800000) /* log(inf) == inf.  */
  42  			return x;
  43  		if ((ix & 0x80000000) || ix * 2 >= 0xff000000)
  44  			return __math_invalidf(x);
  45  		/* x is subnormal, normalize it.  */
  46  		ix = asuint(x * 0x1p23f);
  47  		ix -= 23 << 23;
  48  	}
  49  
  50  	/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
  51  	   The range is split into N subintervals.
  52  	   The ith subinterval contains z and c is near its center.  */
  53  	tmp = ix - OFF;
  54  	i = (tmp >> (23 - LOGF_TABLE_BITS)) % N;
  55  	k = (int32_t)tmp >> 23; /* arithmetic shift */
  56  	iz = ix - (tmp & 0x1ff << 23);
  57  	invc = T[i].invc;
  58  	logc = T[i].logc;
  59  	z = (double_t)asfloat(iz);
  60  
  61  	/* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */
  62  	r = z * invc - 1;
  63  	y0 = logc + (double_t)k * Ln2;
  64  
  65  	/* Pipelined polynomial evaluation to approximate log1p(r).  */
  66  	r2 = r * r;
  67  	y = A[1] * r + A[2];
  68  	y = A[0] * r2 + y;
  69  	y = y * r2 + (y0 + r);
  70  	return eval_as_float(y);
  71  }
  72