The recent discussion on the thread Re: [Maxima] plot numerical question
made me realize that I may be missing something about bigfloats.
Here I compare expr(bfloat(s)) with bfloat( expr(s) ) when
the expression involves factorials.
In the first case the results are equivalent.
In the second case the results differ but with a pattern.
case 1 agreement:
(%i12) e2f(s):=
block([], local(ff),
define(ff(x),factorial(x/4)),
[bfloat(ff(s)), ff( bfloat(s))] )$
(%i13) for i thru 11 do print(i,e2f(i))$
1 [9.06402b-1,9.06402b-1]
2 [8.86226b-1,8.86226b-1]
3 [9.19062b-1,9.19062b-1]
4 [1.0b0,9.99999b-1]
5 [1.133b0,1.133b0]
6 [1.32934b0,1.32934b0]
7 [1.60835b0,1.60835b0]
8 [2.0b0,1.99999b0]
9 [2.54925b0,2.54925b0]
10 [3.32335b0,3.32335b0]
11 [4.42298b0,4.42298b0]
case 2: disagreement with a pattern
(%i14) e3f(s):=
block([ ],local(r4),
define( r4(x), x!/(((x/4)!)^4 * 4^x)),
[bfloat(r4(s)), r4(bfloat(s))] )$
(%i15) for i thru 11 do print(i,e3f(i))$
1 [8.22424b-17,3.70386b-1]
2 [2.02642b-1,2.02642b-1]
3 [2.91763b-17,1.31398b-1]
4 [9.375b-2,9.375b-2]
5 [1.57905b-17,7.11142b-2]
6 [5.62895b-2,5.62895b-2]
7 [1.02074b-17,4.59703b-2]
8 [3.84521b-2,3.84521b-2]
9 [7.27794b-18,3.27769b-2]
10 [2.83699b-2,2.83699b-2]
11 [5.5217b-18,2.48675b-2]
What am I missing??
Ted Woollett