The BBC and Master Computer Public Domain Library

Convert Integer to Floating-Point

Submitted by Steve Fewell

Routine: ConvIWAtoFWA
Name: Convert Integer to Floating-Point
Starting Address: &8185
Entry criteria: The IWA contains an Integer number.
Exit: The value of the IWA has been transferred to the FWA.

Note: The FWA Mantissa is stored Most significant byte first, least significant byte last (the opposite way to Integers).

Description:
Set the FWA Rounding (Mantissa 5) and Exponent Overflow bytes to zero. Store the IWA Sign Byte (?&2D) in the FWA Sign Byte (The top bit of this byte indicates whether the number is positive or negative, and its value is directly transferable between the IWA and FWA).

If the Integer in the IWA is negative, then complement the Integer, and load A with the most significant byte of the Integer (We can deal directly with a positive value as the FWA will be stored as a positive number, with its Sign Byte indicating its sign).

If the Most Significant Byte of the IWA [A] isn't zero, then the number is 4 bytes long, so store IWA Byte 3 in FWA Mantissa Byte 2,  IWA Byte 2 in FWA Mantissa Byte 3 and  IWA Byte 1 in FWA Mantissa Byte 4 (opposite order), then normalise the FWA (Make the Most Significant Bit of the FWA's Mantissa equal to 1, and store A back to FWA Mantissa Byte 1, and Y back to the FWA Exponent), with an initial exponent [Y] value of 160 (that is 2^32, as there are 32 bits in a 4 byte number), and exit.

Otherwise, store zero in FWA Mantissa Byte 4, and check to see if IWA Byte 3 is zero.

If IWA Byte 3 isn't zero, then the number is 3 bytes long, so store IWA Byte 2 in FWA Mantissa Byte 2 and  IWA Byte 1 in FWA Mantissa Byte 3 (opposite order), then normalise the FWA (Make the Most Significant Bit of the FWA's Mantissa equal to 1, and store A back to FWA Mantissa Byte 1, and Y back to the FWA Exponent), with A = IWA Byte 3 and an initial exponent [Y] value of 152 (that is 2^24, as there are 24 bits in a 3 byte number), and exit.

Otherwise, store zero in FWA Mantissa Byte 3, and check to see if IWA Byte 2 is zero.

If IWA Byte 2 isn't zero, then the number is 2 bytes long, so store IWA Byte 1 in FWA Mantissa Byte 2, then normalise the FWA (Make the Most Significant Bit of the FWA's Mantissa equal to 1, and store A back to FWA Mantissa Byte 1, and Y back to the FWA Exponent), with A = IWA Byte 2 and an initial exponent [Y] value of 144 (that is 2^16, as there are 16 bits in a 2 byte number), and exit.

Otherwise, store zero in FWA Mantissa Byte 2 and normalise the FWA (Make the Most Significant Bit of the FWA's Mantissa equal to 1, and store A back to FWA Mantissa Byte 1, and Y back to the FWA Exponent), with A = IWA Byte 1 and an initial exponent [Y] value of 136 (that is 2^8, as there are 8 bits in a 1 byte number). The normalisation will decide whether the number is zero, or a 1-byte number, and adjust the FWA accordingly.

Disassembly for the Convert Integer to Floating-Point routine

Normalise FWA with an initial exponent of 136 (&88)