Name: FFTR2C.ASM
         Type: Assembler Macro
      Version: 1.2
  Last Change:  4-Feb-87

  Description: Radix 2, In-place, Decimation-in-time Complex FFT Macro

 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).
 FFTR2C 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 performed "in-place", meaning that only one data
 buffer is required for both input and output data.  The input
 data is assumed to be in normal (time-sequential) order and the
 output is in bit-reversed order.  By using the reverse-carry
 address modifier and a separate output data buffer, the output
 data may be easily unscrambled.  Other methods also exist to
 unscramble the output data without a separate output data buffer. 
 The FFTR2C 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 FFTR2C macro is faster than the FFTR2A and FFTR2B library
 macros.  The speed increase is obtained by performing the first
 two passes in one combined operation without storing the results
 of the first pass.  The first two passes do not require any
 multiplies since the coefficients are -1, 0 or +1.  The last pass
 is also split out from the triple nested DO loop and given a separate
 DO loop (identical to the FFTR2B macro).  The reason this is faster
 is that the inner loop always starts with a loop count of 1 on the
 last pass.  Note that the separate last pass DO loop uses different
 addressing modes to increment through the butterflies, thus avoiding
 outer loops.  Additional details are included in the source file;
 however, more algorithm description would be required for complete
 understanding by typical users.  The FFTR2C macro can directly
 replace the FFTR2A macro using the calling procedure shown in the
 FFTR2AT test program.