#1135 cf not correct for composed expressions

open
nobody
5
2012-11-18
2007-02-23
Stavros Macrakis
No

cf is grossly wrong for composed expressions. For example:

cf(sqrt(2)*sqrt(3)), cflength=3 => [2,2,4,1,5,1,1,3]
cf(sqrt(6)), cflength=3 => [2,2,4,2,4,2,4]
^^
This is because it first calculates the truncated cf of the parts, and multiplies them. There is no way a priori of knowing which terms in the result are correct. There also seem to be some egregious bugs (which aren't worth fixing because of the above general problem):

expr: sqrt(3)-sqrt(2)\$
float(expr) => 0.318...
cf(expr),cflength=5 => [3, 6, 1, 5, 7, ...
cf(float(expr)) => [0,3,6,1,5...]
float(cfdisrep(cf(expr))), cflength=5 => 3.146...
float(cfdisrep(cf(expr))), cflength=100 => 3.146...

I do not see the usefulness of calculating cf(sqrt(2)*sqrt(3)) as cf(sqrt(2))*cf(sqrt(3)), but perhaps someone else does. I also don't see the usefulness of the cflength parameter as currently defined.

More examples where current code is wrong (and also produces lots of spurious extra terms):

cf(sqrt(2/3)),cflength:12 =>
[0,1,4,2,4,2,4,2,4,2,3,1,281,4,2,1,9,1,3,2,2,14]
^^^ first incorrect term @ position 11
(would be correct if rounded to 11 terms, but not to 12)

(With Andreas Eder's new code):
cf((3/5)^(1/3)),cflength:5 =>
[0, 1, 5, 3, 2, 2, 2]
^^^ first incorrect term @ position 4
cf(100000^(1/3)),cflength:5 == cflength(10*100^(1/3)) =>
[46,2,2,2,8,1,1 ...]
^ first incorrect term @ 3