(12C+) Bernoulli Number

[Albert Chan]

(07-28-2019 11:21 AM)John Keith Wrote:  EDIT: I tried your program as well as the Akiyama-Tanigawa method as used in the third program here on the HP-48G and both methods fail due to catastrophic rounding error for n>10.

If we use scaled numbers, we can push it a bit more.
Example, this is Akiyama-Tanigawa method, scaled by denominator LCM.

Note: XCas 1.9.0 default float now is 48 bits, truncated rounding.
Note: round(L[0]) does not change L[0] value, just its type, real → integer.

XCas> m := 22;
XCas> h := lcm(range(2, m+2))         → 5354228880
XCas> L := float(h ./ range(2, m+2))
XCas> for(k:=2; k<=m; k++) {
                L := -deltalist(L) .* range(1,len(L));
                if (even(k)) print(k, round(L[0])/h);
          };

2,      1/6
4,     -1/30
6,      1/42
8,     -1/30
10,     5/66
12,    -691/2730
14,     7/6
16,    -3617/510
18,     43867/798
20,    -174611/330
22,     854513/138

48 bits float mangaged to get upto B(22)
IEEE double can reach B(24), all exact fractions.