Maxima -- GPL CAS based on DOE-MACSYMA / Bugs / #5197 expand of complex float to high power loses precision

Computer Algebra System written in Common Lisp

#5197 expand of complex float to high power loses precision

Milestone: None

Status: open

Owner: nobody

Labels: simpexpt (13) float (28)

Priority: 5

Updated: 2 hours ago

Created: 2 hours ago

Creator: Stavros Macrakis

Private: No

Expanding a power with complex float base loses a lot of precision.
Compare #4959

expand((1.0+%i)^200);
  => 2.8517e+41 %i - 2.4847e+43

This can be mitigated with more precision:

for fpprec:5 thru 100 step 10 do print( fpprec,expand((1.0b0+%i)^200));

5 3.4721b52 %i + 1.3389b53 
15 7.2764b42 %i - 3.9616b42 
25 4.304b32 %i + 9.9844b31 
35 2.6341b22 %i + 1.2677b30 
45 1.2677b30 - 1.05b12 %i 
55 5.76b2 %i + 1.2677b30 
65 1.2677b30 
75 1.2677b30 
85 1.2677b30 
95 1.2677b30

but a better exponentiation algorithm would be preferable.

Discussion

Stavros Macrakis - 2 hours ago

labels: --> simpexpt
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Stavros Macrakis - 2 hours ago

labels: simpexpt --> simpexpt, float

summary: expand of float to high power loses precision --> expand of complex float to high power loses precision

Description has changed:

Diff:

--- old +++ new @@ -1,4 +1,4 @@ -Expanding a power with float base loses a lot of precision. +Expanding a power with complex float base loses a lot of precision. Compare #4959 ~~~ expand((1.0+%i)^200);
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expand of complex float to high power loses precision

Computer Algebra System written in Common Lisp

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#5197 expand of complex float to high power loses precision

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