[metapost] Strange result for angle() in MP 1.750

[Dan Luecking]

In metapost version 1.750 (just downloaded off SupelectFoundry):
   *show angle (up);
gives me
   >> 1440
This is not only an incorrect angle (dir 1440 = right),
but not in the documented range of -180 to 180.

Version 1.504 correctly produces 90.
Here is some more lunacy regarding angle():
   *show angle (.3,1);
   >> 1172.80957
   *show angle (.5,1);
   >> 1014.95923
   *show angle (1,.8);
   >> 618.55861
   *show angle (1,.6);
   >> 495.4242
   *show angle (1,.4);
   >> 348.81773
   *show angle (1,.2);
   >> 180.9562
   *show angle (1,.1);
   >> 91.375
   *show angle (1,0);
   >> 0
(The last one shows only that even an incorrect calculation
can occasionally produce a correct answer.)

These numbers appear to all be off by a factor of 16,
suggesting the bug is a simple oversight in the implementation
of Knuth's algorithm. His algorithm treats angles internally
as integer multiples of 2^{-20}, making them 16 times the
usual numerics which are integer multiples of 2^{-16}.


Regards,
Dan


Daniel H. Luecking
Department of Mathematical Sciences
Fayetteville, Arkansas
http://www-cs-faculty.stanford.edu/~knuth/iaq.html