         ttl       fast floating point arctangent (ffpatan)
***************************************
* (c) copyright 1981 by motorola inc. *
***************************************
 
*************************************************
*                  ffpatan                      *
*       fast floating point arctangent          *
*                                               *
*  input:   d7 - input argument                 *
*                                               *
*  output:  d7 - arctangent radian result       *
*                                               *
*     all other registers totally transparent   *
*                                               *
*  code size: 132 bytes   stack work: 32 bytes  *
*                                               *
*  condition codes:                             *
*        z - set if the result is zero          *
*        n - cleared                            *
*        v - cleared                            *
*        c - undefined                          *
*        x - undefined                          *
*                                               *
*                                               *
*  notes:                                       *
*    1) spot checks show at least six digit     *
*       precision on all sampled cases.         *
*                                               *
*  time: (8mhz no wait states assumed)          *
*                                               *
*        the time is very data sensitive with   *
*        sample values ranging from 238 to      *
*        465 microseconds                       *
*                                               *
*************************************************
         page
ffpatan  idnt  1,2 ffp arctangent
 
         opt       pcs
 
         section   9
 
         xdef      ffpatan                       entry point
 
         xref      ffptheta                    arctangent table
 
         xref      ffpdiv,ffpsub   arithmetic primitives
         xref      ffptnorm          transcendental normalize routine
         xref      ffpcpyrt            copyright stub
 
piov2    equ       $c90fdb41           float pi/2
fpone    equ       $80000041           float 1
 
********************
* arctangent entry *
********************
 
* save registers and perform argument reduction
ffpatan  movem.l   d1-d6/a0,-(sp)      save caller's registers
         move.b    d7,-(sp)            save original sign on stack
         and.b     #$7f,d7             take absolute value of arg
* insure less than one for cordic loop
         move.l    #fpone,d6           load up 1
         clr.b     -(sp)               default no inverse required
         cmp.b     d6,d7               ? less than one
         bcs.s     fpainrg             branch in range
         bhi.s     fpardc              higher - must reduce
         cmp.l     d6,d7               ? less or equal to one
         bls.s     fpainrg             branch yes, is in range
* argument > 1:  atan(1/x) =  pi/2 - atan(x)
fpardc   not.b     (sp)                flag inverse taken
         exg.l     d6,d7               take inverse of argument
         jsr       ffpdiv              perform divide
 
* perform cordic function
* convert to bin(31,29) precision
fpainrg  sub.b     #64+3,d7            adjust exponent
         neg.b     d7                  for shift necessary
         cmp.b     #31,d7              ? too small to worry about
         bls.s     fpanotz             branch if not too small
         move.l    #0,d6               convert to a zero
         bra.s     fpazro              branch if zero
fpanotz  lsr.l     d7,d7               shift to bin(31,29) precision
 
*****************************************
* cordic calculation registers:         *
* d1 - loop count   a0 - table pointer  *
* d2 - shift count                      *
* d3 - y'   d5 - y                      *
* d4 - x'   d6 - z                      *
* d7 - x                                *
*****************************************
 
         move.l    #0,d6               z=0
         move.l    #1<<29,d5           y=1
         lea       ffptheta+4,a0       to arctangent table
         move.l    #24,d1              loop 25 times
         move.l    #1,d2               prime shift counter
         bra.s     cordic              enter cordic loop
 
* cordic loop
fplpls   asr.l     d2,d4               shift(x')
         add.l     d4,d5               y = y + x'
         add.l     (a0),d6             z = z + arctan(i)
cordic   move.l    d7,d4               x' = x
         move.l    d5,d3               y' = y
         asr.l     d2,d3               shift(y')
fplnlp   sub.l     d3,d7               x = x - y'
         bpl.s     fplpls              branch negative
         move.l    d4,d7               restore x
         add.l     #4,a0               to next table entry
         add.b     #1,d2               increment shift count
         lsr.l     #1,d3               shift(y')
         dbra      d1,fplnlp           and loop until done
 
* now convert to float and reconstruct the result
         jsr       ffptnorm            float z
fpazro   move.l    d6,d7               copy answer to d7
         tst.b     (sp)+               ? was inverse taken
         beq.s     fpaninv             branch if not
         move.l    #piov2,d7           take away from pi over two
         jsr       ffpsub              subtract
fpaninv  move.b    (sp)+,d6            load original sign
         tst.b     d7                  ? result zero
         beq.s     fpartn              return if so
         and.b     #$80,d6             clear exponent portion
         or.b      d6,d7               if minus, give minus result
fpartn   movem.l   (sp)+,d1-d6/a0      restore caller's registers
         rts                           return to caller
 
         end

