This post shows the C implementation of the algorithm in this post.
http://www.8052.com/forum/read.phtml?id=145409

To compare the result of this algorithm with double precision log function on PC, C implementation was applied.
Scan through the entire integer range, 0001H - 0FFFFH, the difference was fit in this precision.
(-2.42371/256, +0/256)

As you can see, the code is easily ported to ASM.

Tsuneo

//
//  Calculation of log10( x )
//      input:  unsigned 16 bit integer
//      output: 16 bit fixed point
//              MSB: integer
//              LSB: decimal
//
//      precision:
//          comparead with double precision floating function
//          -2.42371/256, +0/256
//
typedef unsigned char   uchar;
typedef unsigned int    uint;
typedef unsigned long   ulong;

enum {MSB, LSB};        // big endian: for KEIL
//enum {LSB, MSB};      // little endian: for SDCC
typedef union {         // union to split 2 byte value
    uint  i;
    uchar c[2];
} T2byte;

#define BITS    16          // number of bits
#define LOG2    77          // log10( 2 ) * 256 = 77.0637

//
// Table of log2( x + 1 )   (0 <= x < 1)
//  Actual calculation is
//      y = floor( log2( 1 + n / 256 ) * 256 + 0.5 )
//
static uchar code log2_tbl[] = {
      0,   1,   3,   4,   6,   7,   9,  10,  11,  13,  14,  16,  17,  18,  20,  21,
     22,  24,  25,  26,  28,  29,  30,  32,  33,  34,  36,  37,  38,  40,  41,  42,
     44,  45,  46,  47,  49,  50,  51,  52,  54,  55,  56,  57,  59,  60,  61,  62,
     63,  65,  66,  67,  68,  69,  71,  72,  73,  74,  75,  77,  78,  79,  80,  81,
     82,  84,  85,  86,  87,  88,  89,  90,  92,  93,  94,  95,  96,  97,  98,  99,
    100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 116, 117,
    118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133,
    134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149,
    150, 151, 152, 153, 154, 155, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
    165, 166, 167, 168, 169, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 178,
    179, 180, 181, 182, 183, 184, 185, 185, 186, 187, 188, 189, 190, 191, 192, 192,
    193, 194, 195, 196, 197, 198, 198, 199, 200, 201, 202, 203, 203, 204, 205, 206,
    207, 208, 208, 209, 210, 211, 212, 212, 213, 214, 215, 216, 216, 217, 218, 219,
    220, 220, 221, 222, 223, 224, 224, 225, 226, 227, 228, 228, 229, 230, 231, 231,
    232, 233, 234, 234, 235, 236, 237, 238, 238, 239, 240, 241, 241, 242, 243, 244,
    244, 245, 246, 247, 247, 248, 249, 249, 250, 251, 252, 252, 253, 254, 255, 255
};

uint log10( uint x )
{
    T2byte val;
    T2byte result;
                                // calculation of log2( x )
    val.i = x;
    result.c[MSB] = BITS;
                                // shif left until carry sees '1'
    while ( (val.c[MSB] & 0x80) == 0 ) {
        val.i <<= 1;
        --result.c[MSB];
    }
    val.i <<= 1;
    --result.c[MSB];            // integer part is calculated
                                // get decimal with table
    result.c[LSB] = log2_tbl[ val.c[MSB] ];
                                // convert to log10, with rounding
    return (uint)(( (ulong)result.i * LOG2 + 0x80 ) >> 8);
}