         Name: FFTR2CN.ASM
         Type: Assembler Macro
      Version: 1.0
  Last Change:  18-Aug-88

  Description: Radix 2, Decimation-in-time Complex FFT Macro with normally
               ordered input and output

 This macro performs a complete Fast Fourier Transform (FFT) on complex
 data.  The basic algorithm is the Decimation-in-time (DIT), Radix 2
 FFT algorithm using 24 bit fixed-point arithmetic.  The algorithm uses
 a sine-cosine lookup table for the FFT coefficients (twiddle factors).
 FFTR2CN can be called to perform any FFT from 16-32768 points.  Simply
 call it with the arguments of number of FFT points, location of the
 data array and location of the sine-cosine table.  All register
 initialization is performed by this macro.  However, the macro assumes
 that registers which should not be altered by the FFT have already been
 saved by the main program.  This allows the user to fit the FFT macro
 into his application and thus control the context switching overhead.
 No data scaling is performed and no overflow detection is done.
 Modifications to this routine could allow it to be used with the
 scaling modes and thus allow dynamic scaling for each FFT pass.

 All data and coefficients are complex, with the real part in X Data
 memory and the imaginary part in Y Data memory.  For an N point FFT,
 the data buffer requires N X Data and N Y Data memory locations.
 The algorithm is not performed "in-place", meaning that different data
 buffers are required for input and output data.  The input
 data is assumed to be in normal (time-sequential) order and the
 output is also in normal order.   
 
 The FFTR2CN macro uses "twiddle factors" (-cosine and -sine tables)
 stored in data memory.  For maximum speed, the FFT macro performs
 a lookup table operation to get new sine and cosine values for
 each group of butterflies.  A SINCOS macro is available to
 generate these tables.  For an N point FFT, N/2 X Data and N/2
 Y Data locations are required.  Sine and cosine values could be
 calculated in real-time to save data memory at the expense of
 execution time.

 The FFTR2CN macro is identical to the FFTR2C macro except for the storage
 of the output data. Using the reverse-carry address modifier and a 
 separate output data buffer, the output data is stored in normal order. The
 FFTR2CN macro can directly replace the FFTR2C macro if "odata", the output 
 buffer starting address is specified and included in the call.^Z
