atan2 incorrect for some inputs about cormanlisp

[arbv]

Thank you for your interest in Corman Lisp!

I have replied to you in the Google Group. Unfortunately, we do not have an active mailing list or forum yet.

May I ask you to provide some code which demonstrates the problem? It would simplify the investigation.

[framlingham]

Sure thing. This code loops around a unit circle from 0° to 360° in 15° steps. The last two numbers show the starting angle, and the reconstructed angle using atan. This is run on v3.1.2

(loop for ang from 0 to (* 2 pi) by (/ pi 12)
      for deg = (round (* ang (/ 180 pi)))
      for x = (cos ang)
      and y = (sin ang)
      for atan-ang = (atan y x)
      for atan-deg = (round (* atan-ang (/ 180 pi)))
  do (format t "~&Ang = ~,3Fr  pt = (~5,2F, ~5,2F) start deg = ~3D, atan = ~3D~%" ang x y deg atan-deg))
Ang = 0.000r  pt = ( 1.00,  0.00) start deg =   0, atan =   0
Ang = 0.262r  pt = ( 0.97,  0.26) start deg =  15, atan =  15
Ang = 0.524r  pt = ( 0.87,  0.50) start deg =  30, atan =  30
Ang = 0.785r  pt = ( 0.71,  0.71) start deg =  45, atan =  45
Ang = 1.047r  pt = ( 0.50,  0.87) start deg =  60, atan =  60
Ang = 1.309r  pt = ( 0.26,  0.97) start deg =  75, atan =  75
Ang = 1.571r  pt = ( 0.00,  1.00) start deg =  90, atan =  90
Ang = 1.833r  pt = (-0.26,  0.97) start deg = 105, atan = -75
Ang = 2.094r  pt = (-0.50,  0.87) start deg = 120, atan = -60
Ang = 2.356r  pt = (-0.71,  0.71) start deg = 135, atan = -45
Ang = 2.618r  pt = (-0.87,  0.50) start deg = 150, atan = -30
Ang = 2.880r  pt = (-0.97,  0.26) start deg = 165, atan = -15
Ang = 3.142r  pt = (-1.00, -0.00) start deg = 180, atan =   0
Ang = 3.403r  pt = (-0.97, -0.26) start deg = 195, atan =  15
Ang = 3.665r  pt = (-0.87, -0.50) start deg = 210, atan =  30
Ang = 3.927r  pt = (-0.71, -0.71) start deg = 225, atan =  45
Ang = 4.189r  pt = (-0.50, -0.87) start deg = 240, atan =  60
Ang = 4.451r  pt = (-0.26, -0.97) start deg = 255, atan =  75
Ang = 4.712r  pt = (-0.00, -1.00) start deg = 270, atan =  90
Ang = 4.974r  pt = ( 0.26, -0.97) start deg = 285, atan = -75
Ang = 5.236r  pt = ( 0.50, -0.87) start deg = 300, atan = -60
Ang = 5.498r  pt = ( 0.71, -0.71) start deg = 315, atan = -45
Ang = 5.760r  pt = ( 0.87, -0.50) start deg = 330, atan = -30
Ang = 6.021r  pt = ( 0.97, -0.26) start deg = 345, atan = -15
Ang = 6.283r  pt = ( 1.00, -0.00) start deg = 360, atan =   0
NIL

The existing atan only works in the first quadrant (and fourth quadrant I suppose), and I think needs updating like in my diff. In developing the suggested code, I generated output and compared it to other calculations, like Excel's atan2. I found that if I wasn't careful, I got an inconsistent shape of the atan graph.

[arbv]

Thanks, that is a good catch. With your fix Corman Lisp produces the same results as SBCL.