The BBC and Master Computer Public Domain Library

8368 Floating-Point Addition

Submitted by Steve Fewell

Routine:aplus1
Name: Floating-Point Addition (FWA=FWA+FWB Normalised & Unrounded)
Starting Address: &8368
Entry criteria: The FWA and FWB contain the required numbers.
Exit: The FWA contains the result.

Description:

If FWA Mantissa byte 1 = 0 then FWA= 0.0, so return FWB
in FWA (AcopyB routine).

A = FWA Exponent - FWB Exponent
If exponents are equal then goto 83E2 to do the addition.

If the FWA exponent > FWB exponent then goto 83A9 to adjust the exponents to be equal.
This routine does the following:
  Inverse and increment (by 1) the exponent difference. This will make it a two's
  complement value and complement the value (exponent diff=-exponent diff).
  If the exponent difference > &24 then the FWA is too small to add, so return FWA=FWB.
  
  Otherwise, Set the Results exponent [FWA exponent] = FWB exponent.

  If the exponent difference is a multiple of 8 (8, 16, 24, 32) then shift
  the FWA mantissa right a byte [divide FWA Mantissa by 16] and reduce the
  exponent diference by 8. [Keep doing this until FWA exponent = FWB exponent].

  If the exponent difference is zero (it will be if the byte shifting was done (above))
  then do the addition [83E2].
  Otherwise shift the FWA Mantissas bits right a bit [divide Mantissa by 2] and decrement
  the exponent difference. Repeat this until the difference is zero.

Lastly, goto 83E2 to do the additional as the exponents are now equal.

Otherwise, (FWB exponent > FWA exponent) so need to make the exponents equal as follows:
  If the exponent difference > &24 then the FWB is too small to add, so return with FWA unchanged.
  
  Otherwise, if the exponent difference is a multiple of 8 (8, 16, 24, 32) then shift
  the FWB Mantissa right a byte [divide FWA Mantissa by 16] and reduce the
  exponent diference by 8. [Keep doing this until FWB exponent = FWA exponent].

  If the exponent difference is zero (it will be if the byte shifting was done (above))
  then do the addition [83E2].
  Otherwise shift the FWB Mantissa right one bit [divide Mantissa by 2] and decrement
  the exponent difference. Repeat this until the difference is zero.

Lastly, goto 83E2 to do the additional as the exponents are now equal.

83E2: Addition (where the exponents are equal):
A = FWA Sign; EOR with FWB Sign.
If different signs then goto 83EC to do subtraction (described below).

Clear carry and jump to &A447 (in Floating-Point Multiply by 10 routine).
A447 does the following:
  FWA Mantissa 5 = FWA Mantissa 5 + FWB Mantissa 5
  FWA Mantissa 4 = FWA Mantissa 4 + FWB Mantissa 4
  FWA Mantissa 3 = FWA Mantissa 3 + FWB Mantissa 3
  FWA Mantissa 2 = FWA Mantissa 2 + FWB Mantissa 2
  FWA Mantissa 1 = FWA Mantissa 1 + FWB Mantissa 1

  If no overflow from adding the Mantissas then end (RTS).
  (Note: The exponent and sign bytes are unchanged as they are the same for both numbers.)
  Otherwise, divide the Mantissa by 2 (keeping the top bit set) & increment exponent.

83EC: Signs are not equal - do subtraction:
If FWA = FWB then Clear FWA to return with FWA = 0.0 (numbers add to zero)
else 840D: If FWA > FWB then goto 8435 (Subtract FWA from FWA) [Described below]

Otherwise, copy the FWB sign to FWA sign (as the result will have the same sign as FWB)
& subtract FWA Mantissa from FWB Mantissa storing the result in the FWA Mantissa.
Jump to &81F9 to Normalise FWA (A = FWA Mantissa 1 on entry)

8435: Subtract FWB Mantissa from FWA Mantissa:
This routine subtracts the FWB value from FWA, keeping the FWA Exponent and FWA sign unaltered
as the result will have the same sign as the FWA.

Subtract FWA Mantissa from FWB Mantissa storing the result in the FWA Mantissa.
Jump to &81F9 to Normalise FWA (A = FWA Mantissa 1 on entry)

Disassembly for the Floating-Point Addition routine