#1931 rectform loses some accuracy

[Raymond Toy]

Consider:

rectform(1e300/(1e300+3/2*%i)) -> 1.0

But

float(rectform(10^300/(10^300+3/2*%i))) -> 1.0 - 1.5e-300 * %i

The inaccuracy is caused by Maxima computing the rectform in two parts. Maxima computes 1/(1e300+3/2*%i) and then multiplies by 1e300. Maxima correctly computes 1/(1e300+3/2*%i) as 1e-300. But doing it in two steps causes the very tiny imaginary part to be lost.

[Dieter Kaiser]

For the record:

With SBCL and Maxima 5.25post I get for the example an overflow error:

(%i1) rectform(1e300/(1e300+3/2*%i));

Maxima encountered a Lisp error:
arithmetic error FLOATING-POINT-OVERFLOW signalled
Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.

I have tried the biggest possible exponent:

(%i31) float(rectform(1e154/(1e154+3/2*%i)));
(%o31) 1.0 - 1.5e-154 %i
(%i32) float(rectform(10^154/(10^154+3/2*%i)));
(%o32) 1.0 - 1.5e-154 %i

Dieter Kaiser

[Raymond Toy]

That's odd. I tried it with sbcl, and it had no problems with overflow with the given examples.

More investigation needed.

[Dieter Kaiser]

Sorry, but today I have checked the example again. Now I get the described results with SBCL:

Maxima version: 5.25post
Maxima build date: 19:8 8/14/2011
Host type: i686-pc-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.45

(%i5) rectform(1e300/(1e300+3/2*%i));
(%o5) 1.0
(%i9) float(rectform(10^300/(10^300+3/2*%i)));
(%o9) 1.0-1.5e-300*%i

Perhaps, I had some own code in my sandbox. I think I have tried to use the bigfloat-package.

Dieter Kaiser