# Bhaskara sin angle reduction
          # pretty print from autoindent and ased editor
          # Bhaskara sine formula and extensions into TCL
          # written on Windows XP on  TCL
          # working under TCL version 8.5.6
          # gold on TCL WIKI , 10jan2017
          # angle reduction from k-N*360 degrees, -360> output angle < 360 
       proc sin_angle_reduction {aa } {set pi [ expr { acos(-1) } ];   expr {abs($aa)>360? asin ( sin($aa*($pi/180.)) ) * (180./$pi) : $aa }  }
           puts " sin angle reduction [ sin_angle_reduction  30.    ]  "
           puts " sin angle reduction [ sin_angle_reduction   760.  ]  "   
           puts " sin angle reduction [ sin_angle_reduction  -760.  ]  "
           puts " timing  sin angle reduction [ time {sin_angle_reduction  -760. } 100 ] "  
           puts " timing degree_reduction   [ degree_reduction   900005.0000000000001  ] "   
           puts " timing degree_reduction   [ time {degree_reduction   900055.0000000000001 } 100 ] "   
           # sin angle reduction 30.0
           #sin angle reduction 40.00000000000003
           #sin angle reduction -40.00000000000003
           #timing  sin angle reduction 5.7 microseconds per iteration
           #timing degree_reduction   4.98 microseconds per iteration