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+==== 2LOG, calculate binary logarithm ====
+The 2LOG routine was the result of the need for converting a linear input into something with a more logarithmic character. There was no need for high accuracy, but rather a short reliable routine. The routine uses a very simple principle, but the result is surprisingly useable. A prime example where focussing on the essentials results in an excellent solution.
+The 2LOG routine produces as output a fixed floating point number with 8 bits after the decimal point. ( x...x**.**xxxxxxxx ) The number of bits before the decimal point depends on the native width of the stack.
+=== The principle used is this: ===
+looking at the number to be converted in binary representation: (see grafic below) - step 1: take the bit-position+1 of the first set bit as number before the decimal point - step 2: as 8 bit fraction take the highest 8 bits following the most most significant set bit. If there are less than 8 bits, pad the end with cleared bits up to 8 bits.
+It is good to notice that the fractional part forms a linear interpolation between two consecutive log numbers. For most purposes that is accurate enough.
+<html><img src="https://user-images.githubusercontent.com/4964288/167205050-76579ac1-2707-4037-9d6d-2a5452b601b5.png" alt="drawing" width="500" height="250"/></html>
+=== the generic Forth program ===
+As example we look at the routine for a 16b Forth. The other example is suitable for all Forth implementations.
+<code forth>
+decimal
+: 2LOG16b ( u -- y )
+0 do
+        s>d if
+* 8 rshift                 \ linear interpolation
+i -                      \ logarithmic class
+lshift or leave
+        then 2*
+    loop ;
+</code>
+  * The programs does maximal 16 loops.
+  * For each loop S>D is used to check if the most significant bit is set. If not, then the program shifts the number 1 bit to the left with 2*.
+  * Otherwise it calculates the output.
+    * The logarithmic part is calculated by subtracting the index from 15.
+    * The fractional part is calculated by shifting to left with 1bit, followed by shifting 8 bits to the right.
+  * Finally, both numbers are then combined into one number with a shift and or as final output.
+=== The general version ===
+The general version is suitable for all Forth-implementations which have a multiple of 8 bits as cell-width. It functions in exactly the same way as the 16b example above. But during compilation it calculates the, for that Forth-implementation relevant, values for the do**...**loop, shift and subtraction.
+<code forth>
+: 2LOG ( u -- y )
+    [ 8 cells ] literal 0 do                \ #bits/cell
+        s>d if  2*
+            [ 8 cells 8 - ] literal rshift  \ linear interpolation
+            [ 8 cells 1- ]  literal  i -    \ logarithmic class
+lshift or leave
+        then 2*
+    loop ;
+</code>
+==== Contributions ====
+<html><h2 style="background-color:yellow">Alternative Implementations</h2></html>