Re: modify coord-rotate to get exact values for (sin PI) etc (issue 269530043 by address@hidden)

[dak]

https://codereview.appspot.com/269530043/diff/40001/scm/lily-library.scm
File scm/lily-library.scm (right):

https://codereview.appspot.com/269530043/diff/40001/scm/lily-library.scm#newcode721
scm/lily-library.scm:721: (moved-angle (- angle (/ (* quadrant PI) 2)))
Ok, let's just tackle this as a theoretical exercise since I remain
unconvinced that we are doing ourselves much of a favor straying from
degrees except at the final step.  Then angle-0-2pi is basically an
independent source of numerical ambiguity we want to avoid.  So I'd
probably do it as follows:

(let* ((quadrant
        (inexact->exact (round (/ angle PI/2))))
       (moved-angle (- angle (* quadrant PI/2)))
       (s (sin moved-angle))
       (c (cos moved-angle))
       (x (coord-x coordinate))
       (y (coord-y coordinate)))
  (case (modulo quadrant 4)
    ((0) % -45 .. 45
     (cons ...))
    ((1) % 45 .. 135
     (cons ...))
    ((2) % 135 .. 225
     (cons ...))
    ((3) % 225 .. 315
     (cons ...))))

Note that this retains the problem that (* quadrant PI/2) might just
not be properly representable which can make the whole exercise end up
still not delivering perfect values for 3*PI/2 or 5*PI/2 or similar,
depending on just how those values were arrived at.  However,

(* exact-integer PI/2) likely has about the best chance to match
values that the user arrived with using similar expressions of his
own.  I'd also don't make two separate case statements for cos and sin
since that's likely a construct that is a bit expensive.

https://codereview.appspot.com/269530043/diff/40001/scm/lily-library.scm#newcode751
scm/lily-library.scm:751: (cyclic-base-value (+ value cycle) cycle))
On 2015/10/20 23:06:58, thomasmorley651 wrote:
> what are those red dots??
> Never seen them before.

Spaces before tabs would be my guess.  Or just generally a spacing
change.  either of the two.

https://codereview.appspot.com/269530043/