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Setting longer default decimal precision in python?

+5 votes
1,264 views

Using 1/3 as an example,

 >>> 1./3
0.3333333333333333
 >>> print "%.50f" % (1./3)
0.33333333333333331482961625624739099293947219848633
 >>> print "%.50f" % (10./3)
3.33333333333333348136306995002087205648422241210938
 >>> print "%.50f" % (100./3)
33.33333333333333570180911920033395290374755859375000

which seems to mean real (at least default) decimal precision is limited to "double", 16 digit precision (with rounding error). Is there a way to increase the real precision, preferably as the default?
For instance, UBasic uses a "Words for fractionals", f, "Point(f)" system, where Point(f) sets the decimal display precision, .1^int(ln(65536^73)/ln(10)), with the last few digits usually garbage.
Using "90*(pi/180)*180/pi" as an example to highlight the rounding error (4 = UBasic's f default value):

 Point(2)=.1^09: 89.999999306
 Point(3)=.1^14: 89.9999999999944
 Point(4)=.1^19: 89.9999999999999998772
 Point(5)=.1^24: 89.999999999999999999999217
 Point(7)=.1^33: 89.999999999999999999999999999999823
 Point(10)=.1^48: 89.999999999999999999999999999999999999999999997686
 Point(11)=.1^52: 89.9999999999999999999999999999999999999999999999999632

If not in the core program, is there a higher decimal precision module that can be added?

posted Nov 18, 2013 by Garima Jain

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1 Answer

+1 vote

Python floats actually are implemented as C doubles. And they're not configurable.

However, Python also has a Decimal class, which (unlike floats) are actually decimal rather than binary, and include configurable precision. There is a performance hit -- prior to Python version 3.3, Decimal was
quite slow, but in 3.3 they got a major speed increase and are now nearly as fast as floats.

An example:

py> import decimal
py> x = decimal.Decimal(1)/3
py> decimal.getcontext().prec = 50
py> y = decimal.Decimal(1)/3
py> print(x, y)
0.3333333333333333333333333333 
0.33333333333333333333333333333333333333333333333333
answer Nov 18, 2013 by Naveena Garg
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+1 vote

Comparing floats to Fractions gives unexpected results:

# Python 3.3
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but:

py> 1/3 == float(Fraction(1, 3))
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I expected that float-to-Fraction comparisons would convert the Fraction to a float, but apparently they do the opposite: they convert the float to a Fraction:

py> Fraction(1/3)
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Trivial question, please help.

I need to convert a string literal like "111.25" to floating point number.
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+3 votes

See the following code

void main(){
   float a=5.2;
  if(a==5.2)
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