There is an exp table in the hub at $D000, 12 bits in, 16 bits out. I'm attaching a little demo program to show how it works.
For most problems it gets you only part of the way to your answer and the question about the range of x and y is very important. Look at it this way. The hub exp table gives you 2x for values of x between 0 and 1. So 2x is between 1 and 2. For powers outside that range you have to scale. Add or subtract integer values from the exponent to make the fractional part fall in range for the table. The integer powers you subsequently handle with right or left shifts of the answer that comes out of the table lookup. For other bases, for example ex, you have to dust of high school algebra and recall that ex = 2lg2(e)*x = 21.442695 * x. After multiplying out the exponent, then do the thing with powers of 2 and the table lookup.
When you say "in Spin" are you adverse to loading a floating point cog? Both Float32 and F32 do have exp base e, and base 10, and both internally are interpolating in the base 2 hub tables.
Floating point is at its heart represents a number as a binary fraction between 0 and 1, along with an exponent, so it is preconditioned to use the tables. Here is the start of the Float32 pasm exp function:
[SIZE=1][FONT=courier new]_Exp call #_FMulI ' e ** fnum
long 1.442695041
jmp #_Exp2
_Exp10 call #_FMulI ' 10 ** fnum
long 3.321928095
_Exp2 call #_Unpack ' unpack variable
[/FONT][/SIZE]
You see right there the conversion factor 1.442695041 that will return a base e result, and 3.321928095 for base 10, and then it jumps to the base 2 routine that does the table lookup, adjusts the exponent, and manages the details.
TinkersALot
Posts: 535
Comments
I am thinking you are looking for x^y generally, or e^x? e^x for a narrow range of values could I think best be a lookup table with interpolation.
For most problems it gets you only part of the way to your answer and the question about the range of x and y is very important. Look at it this way. The hub exp table gives you 2x for values of x between 0 and 1. So 2x is between 1 and 2. For powers outside that range you have to scale. Add or subtract integer values from the exponent to make the fractional part fall in range for the table. The integer powers you subsequently handle with right or left shifts of the answer that comes out of the table lookup. For other bases, for example ex, you have to dust of high school algebra and recall that ex = 2lg2(e)*x = 21.442695 * x. After multiplying out the exponent, then do the thing with powers of 2 and the table lookup.
Floating point is at its heart represents a number as a binary fraction between 0 and 1, along with an exponent, so it is preconditioned to use the tables. Here is the start of the Float32 pasm exp function:
[SIZE=1][FONT=courier new]_Exp call #_FMulI ' e ** fnum long 1.442695041 jmp #_Exp2 _Exp10 call #_FMulI ' 10 ** fnum long 3.321928095 _Exp2 call #_Unpack ' unpack variable [/FONT][/SIZE]You see right there the conversion factor 1.442695041 that will return a base e result, and 3.321928095 for base 10, and then it jumps to the base 2 routine that does the table lookup, adjusts the exponent, and manages the details.