The BBC and Master Computer Public Domain Library

A861 Evaluate continued-fraction expansions Series

Submitted by Steve Fewell

Routine:EvaluateSeries
Name: Evaluate continued-fraction expansions Series
Starting Address: &A861
Entry criteria: The FWA contains the value to apply the Number Series to.
Y contains the number of cycles to evaluate.
X contains the LSB address of the first Floating-Point constant (in the FP constant table: &BF24)
to use in the series calculation. This value and subsequent values will be used.
A contains the LSB address of the Floating-Point constant value to set the FWA to
if the number in the FWA is too small to evaluate.
Exit: The FWA contains the result of the calculation.

Description:

Set &47 to the number of cycles that we need to evaluate (Y).
Set &4C to the LSB address of the first Floating-Point constant to use (X).
All Floating-Point constant values used are located in the Floating-Point constant table.

If the exponent of the FWA is less than &40, then the value is too small to evaluate, so set
the FWA to the default value specified (The Floating-Point constant located at &BF00 + A)
and exit. Note: This will also trap a 0.0 value, and thus avoid a Division by zero error when
the reciple value is calculated.

Obtain the reciple of the FWA value (FWA = 1/FWA).
Store the reciple value in the temporary Floating-Point variable located at &046C.

Set argp to the address of the first Floating-Point constant in the series calculation:
that is &BF00 + the LSB value in &4C.
Add the first Floating-Point constant value to the Reciple value in the FWA (FWA=argp+FWA).

For each cycle do the following: [i.e. if the cycle (&47) is 2 then repeat twice]
  * Update argp to point to the address of the next Floating-Point constant (i.e. add
    5 to the LSB address and update &4C to the new LSB address. The MSB
    address is always #&BF). Divide this Floating-Point constant value by
    the FWA (FWA = argp/FWA).
  * Update argp to point to the address of the next Floating-Point constant (i.e. add
    5 to the LSB address and update &4C to the new LSB address. The MSB
    address is always #&BF). Add this Floating-Point constant value to
    the FWA (FWA = argp+FWA).
  * Add the Temporary Floating-Point variable at &046C (the reciple of the original
    value) to the FWA (FWA = argp + FWA).
  * Decrement the cycle number (&47).

Lastly perform a division and addition calculation with the next two floating-point
constants, as follows:
Update argp to point to the address of the next Floating-Point constant (i.e. add 5 to
the LSB address and update &4C to the new LSB address. The MSB address is always #&BF).
Divide this Floating-Point constant value by the FWA (FWA = argp/FWA).
Update argp to point to the address of the next Floating-Point constant (i.e. add 5 to
the LSB address and update &4C to the new LSB address. The MSB address is always #&BF).
Add this Floating-Point constant value to the FWA (FWA = argp+FWA).

The FWA now contains the required result.

Disassembly for the Evaluate continued-fraction expansions series routine