How to increase decimal precision with 'exotic' functions?

Question

I can't figure out how to specify my decimal precision for logs, importing decimal and setting the context does not affect the log functions.

from decimal import *
getcontext().prec = 54

print(Decimal(197)/ Decimal(83))
2.37349397590361445783132530120481927710843373493975904

print(math.log(Decimal(197)))
5.2832037287379885

I would like to set a high precision for functions other than fractions. Python 3 btw.

Answer 1

Possible solutions:

String formatting:

• f-strings have the benefit of not requiring another package to be imported
• f-Strings: A New and Improved Way to Format Strings in Python
• Extend the decimal places shown, to the same extent as the decimal module

x = 4567.09710599898797936589076897
y = 2445.89790870380808990080797897

Lengthen:

print(f'{(x/y):.054f}')
>>> 1.867247643389702504990168563381303101778030395507812500

calculation = math.log(197)
print(f'{calculation:.050f}')
>>> 5.28320372873798849155946300015784800052642822265625

Shorten:

print(f'{(x/y):.02f}')
>>> 1.87

numpy:

• numpy.round

Shorten:

print(np.round(x/y, 2))
>>> 1.87

Lengthen:

• numpy does not extend the precision shown, beyond what's shown by python.

print(np.around(x/y, 54))
>>> 1.8672476433897025

print(x/y)
>>> 1.8672476433897025

decimal Module:

• Decimal fixed point and floating point arithmetic

Example from the question:

print(math.log(197))
>>> 5.2832037287379885

print(math.log(Decimal(197.0)))
>>> 5.2832037287379885

print(Decimal(math.log(197)))
>>> 5.28320372873798849155946300015784800052642822265625

print(Decimal(197).ln())
>>> 5.283203728737988506779797329

print(f'{math.log(197):.050f}')
>>> 5.28320372873798849155946300015784800052642822265625

Notes:

• Either method can be used to format the number to the required decimal place, prior to writing into a log.
• Caveat: due to the way numbers are represented in computers, I'm doubtful if increasing the number of decimal places shown, increases the precision.
  • Floating Point Arithmetic: Issues and Limitations
• Using f-strings provided the same final output precision as using the decimal module.