#395 sign(sqrt(2)/2 - 1/sqrt(2)) => zero, pos, neg, or pnz

[Barton Willis]

Depending on the values of fpprec and signbfloat,
sign(sqrt(2)/2 - 1/sqrt(2)) evaluates to zero, pos,
neg, or pnz.

(C1) display2d : false;

(D1) FALSE
(C2) a : sqrt(2)/2 - 1/sqrt(2);

(D2) SQRT(2)/2-1/SQRT(2)
(C3) for k : 20 thru 25 do (fpprec : k, print(k,sign(a)));

20 ZERO
21 POS
22 ZERO
23 POS
24 ZERO
25 NEG
(D3) DONE
(C4) sign(a), signbfloat : true;

(D4) NEG
(C5) sign(a), signbfloat : false;

(D5) PNZ

Here is another example -- this time sign(p) should
evaluate to pos.

(C7) p : exp(x) - sum(x^k/k!,k,0,15)$

(C8) p : subst(1/10000001,x,p)$

(C9) sign(p),signbfloat : true;

(D9) ZERO
(C10) sign(p),signbfloat : false;

(D10) PNZ
(C11) for k : 20 thru 25 do (fpprec : k, print(k,sign
(p)));

20 POS
21 NEG
22 NEG
23 ZERO
24 POS
25 ZERO
(D11) DONE
(C12)

Additionally, signbfloat isn't documented

(C17) describe("signbfloat");

(D17) FALSE

Barton

[Stavros Macrakis]

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About the specific case of sqrt(2)/2 - 1/sqrt(2), cf. bug
721575 -- they should really simplify to a standard form and
cancel. The general problem of using approximate arithmetic
to check sign/is remains.

[Robert Dodier]

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user_id=501686

The p : exp(x) - sum(x^k/k!,k,0,15)$ etc stuff is still
present in 5.9.3cvs.

Now sqrt(2)/2 - 1/sqrt(2) simplifies to 0, so that one has
gone away.

Incrementing the priority since sign problems are pervasive
and important.