(HP15C)(HP67)(HP41C) Bernoulli Polynomials

[Albert Chan]

(08-31-2023 06:43 PM)Albert Chan Wrote:  For XCas, both 48 bits and IEEE double version, B0(float(16)) give correctly rounded result.

Not in XCas with higher precision, even though MPFR guaranteed correctly rounded result.

XCas> Digits := 16
XCas> 21 / float(7) - 3      → ≈ 2.220e-16      ???

XCas> Digits := 100
XCas> 21 / float(7) - 3      → ≈ 2.286e-100     ???

When I run B0(16) with Digits := 16, which has 54-48 = 6 bits more room, I get:

XCas> Digits := 16;
XCas> float(B0(16)), B0(float(16))

-7.092156862745098, -7.101414149575914

Same result for XCas 1.5.0 and 1.9.0. I think this is a serious bug.