Enter:
(%i2) fpprec:30;
(%o2) 30
(%i3) bfloat((45.12*34.78923)^2);
(%o3) 2.46392687692829128354787826538b6
2.46392687692829131776b6 is the correct value.
build_info("5.27.0","2012-05-08 11:27:57","i686-pc-mingw32","GNU Common Lisp (GCL)","GCL 2.6.8")
Regards
Chris
Raymond Toy
2012-07-22
Can you explain why you think the value you give is the correct value?
Consider this transcript:
(%i1) fpprec:30;
(%o1) 30
(%i2) trace(bfloat);
(%o2) [bfloat]
(%i3) bfloat((45.12*34.78923)^2);
1 Enter bfloat [2463926.876928291]
1 Exit bfloat 2.46392687692829128354787826538b6
(%o3) 2.46392687692829128354787826538b6
Thus, the simplifier has simplified the float expression before bfloat gets a chance to look at it.
christoph reineke
2012-07-23
Sorry, but I don’t understand you.
<Can you explain why you think the value you give is the correct value?>
Which value?
(45.12*34.78923)^2=2.46392687692829131776b6=the correct value.
Since I expect that the correct value has more than 16 digits after the comma,
I use bfloat and fpprec=30.
I quote from the documentation:
“bfloat (expr) Function
Converts all numbers and functions of numbers in expr to bigfloat numbers. The
number of significant digits in the resulting bigfloats is specified by the global
variable fpprec.” …all numbers…!!
Now Maxima returns 30 digits, but the result is wrong. That’s all.
<Thus, the simplifier has simplified the float expression…>
Which simplifier?
If a CAS computes a simple multiplication each digit of the displayed
floating point number should be correct (apart from the last), no matter how
many digits the user wants. Even if I erroneously “simplify” something, Maxima
should never display a wrong result. That’s my opinion.
How do I get the correct result?
Thanks for your help!
Raymond Toy
2012-07-23
When you write 45.12, maxima converts that to a floating point number. But 45.12 cannot be represented exactly in floating point. Same for 34.78923. (You can see what the actual value is by using rationalize(45.12), which is close t o 4512/100, but not the same.)
So maxima uses floating-point arithmetic to compute (45.12*34.78923)^2. Then that floating point number is converted to a bfloat, giving the result that maxima produces.
If you want exact results, use exact rational arithmetic:
bfloat((4512/100 * 3478923/100000)^2);
2.46392687692829131776b6
Of course, even that is an approximation because the exact result is 240617859075028449/97656250000, and that can't be represented exactly as a bfloat.
christoph reineke
2012-07-24
Thanks for your comment, but I’m still convinced that there
is a bug somewhere.
Please take a look at the following numbers:
(%i1) bfloat(1.23456789123456789123456789123456789),fpprec:20;
(%o1) 1.2345678912345678935b0
(%i2) bfloat(1.23456789123456789123456789123456789),fpprec:30;
(%o2) 1.23456789123456789347699213977b0
(%i3) bfloat(1.23456789123456789123456789123456789),fpprec:40;
(%o3) 1.23456789123456789347699213976738974452b0
(%i4) bfloat(1.23456789123456789123456789123456789),fpprec:50;
(%o4) 1.2345678912345678934769921397673897445201873779297b0
The trouble begins after the second 9 with the sequence …3476…,
which should be…1234…
As you see, it doesn’t matter if fpprec=20,30,40 or 50, the
precision is always the same!
That ain’t got nothing to do with our binary system,
fpprec doesn’t work properly.
Maxima cannot handle long decimals (more than 17/18 places after
the decimal point) and that’s a bug.
The function fpprec seems to work if you have to compute real
numbers like sqrt(2) or log(3). It never works if you enter
long decimals.
Raymond Toy
2012-07-24
There's a misunderstanding on how maxima works. Maxima parses 1.23456789123456789123456789123456789 as an IEEE double precision float, essentially independent of how many extra digits you write out. This number is the exact rational (given by rationalize) 5559999494927579/4503599627370496.
When this is converted to a bfloat with a given value of fpprec, the ratio is essentially multiplied by a power of two. When it's printed, these extra digits are produced.
If you really want a bfloat with the given digits, use 1.2345...b0.
Whether maxima should work this way or not is a different question. That would probably be better discussed on the maxima mailing list as a feature request.
Raymond Toy
2012-07-31
Raymond Toy
2012-07-31
Marking as pending/invalid.
Raymond Toy
2012-08-13