### Fast exp2 approximation

References : Posted by Laurent de Soras
Notes :
Partial approximation of exp2 in fixed-point arithmetic. It is exactly :
[0 ; 1[ -> [0.5 ; 1[
f : x |-> 2^(x-1)
To get the full exp2 function, you have to separate the integer and fractionnal part of the number. The integer part may be processed by bitshifting. Process the fractionnal part with the function, and multiply the two results.
Maximum error is only 0.3 % which is pretty good for two mul ! You get also the continuity of the first derivate.

-- Laurent
Code :
// val is a 16-bit fixed-point value in 0x0 - 0xFFFF ([0 ; 1[)
// Returns a 32-bit fixed-point value in 0x80000000 - 0xFFFFFFFF ([0.5 ; 1[)
unsigned int fast_partial_exp2 (int val)
{
unsigned int   result;

__asm
{
mov eax, val
shl eax, 15           ; eax = input [31/31 bits]
or  eax, 080000000h   ; eax = input + 1  [32/31 bits]
mul eax
mov eax, edx          ; eax = (input + 1) ^ 2 [32/30 bits]
mov edx, 2863311531   ; 2/3 [32/32 bits], rounded to +oo
mul edx               ; eax = 2/3 (input + 1) ^ 2 [32/30 bits]
add edx, 1431655766   ; + 4/3 [32/30 bits] + 1
mov result, edx
}

return (result);
}