The BBC and Master Computer Public Domain Library

Convert Floating-Point to Integer

Submitted by Steve Fewell

Routine: ConvFWAtoInt
Name: Convert Floating-Point to Integer
Starting Address: &8242
Entry criteria: The FWA contains a Floating-Point number.
Exit: The FWA value has been truncated, and the Integer part of its value has been retained.

Description:
Load A with the FWA Exponent Byte, if it isn't negative (offset by &80) then the Floating-Point value is less than or equal to zero, so jump to Clear FWA and exit with the Integer value set to zero.

If the FWA Mantissa byte 1 is zero then assume that the FWA contains the value zero [?], so exit by doing an Integer Reverse Order Complement of the FWA's Mantissa value. I'm not sure why this is necessary though, as if the number zero doesn't need to be stored in twos complement form.

Now, keep on moving the bite in the FWA Mantissa right one position, until we are left with the Integer part of the number (Stored most significant Byte first, and least significant Byte in ?&34). This achieves two goals, first it gets rid of the fractional part of the number, and second it right-aligns the Integer value and prefixes it with leading zeros (The Integer value will still be stored the opposite way around to an Integer in the IWA though!).
Here is a comparison showing how a Twos-Complement Integer value is stored in the IWA, and how it is stored in the FWA:

Note: The Floating-Points exponent is the number of bits which make up the Integer part of the number offset by &80 (128). Additionally, the FWA Mantissa Rounding Byte is ignored during this conversion.

To achieve the two goals stated above, BASIC does the following:
Keep dividing the FWA Mantissa by 2 (Moving the bits right one position, making the first bit zero, and loosing the last bit) and incrementing the exponent (Stored in the Accumulator), so that the exponent still  points to the imaginary decimal point which separates the Integer part from the fractional part, until the exponent is 32 (&A0). I.e. This occurs when the start of the fraction has just been moved out of the end of the Mantissa and lost.
This operation (divide Mantissa by 2 and Increment Exponent)  is done once at the beginning, but then if more than 7 bits need to be shifted right, then the alternative quicker method (Divide Mantissa by 16 and Add 8 to Exponent) is used [i.e. move the Mantissa bytes along one place, loosing the last (?&34) byte]. If less than 8 bits need to be shifted, then the single-bit method is used.

If at any point the exponent goes over &A0, then a Too Big error is produced (as the number is > 32 bits long), otherwise, when the exponent is equal to &A0, the Exponent [A] is stored back in the FWA Exponent Byte and an Integer Reverse Order Complement is done (which converts the Integer into Twos-complement notation if a negative result is required - i.e. if the FWA's Sign Byte is negative).

Disassembly for the Convert Floating-Point to Integer routine

Jump to Clear FWA

Move the fractional value from the FWA to the FWB

Jump to "Too Big" error

Check Exponent and make Twos Complement Integer (if necessary)