ocopa - 9 months ago 30

Python Question

The Following code examples my problem which does not occur between 10 power 10 and 10 power 11, but does for the example given in code and above it.

I can't see where in my code I am not properly handling the retrieval of the original value. May be I have just missed something simple.

I need to be sure that I can recover

`x`

`log x`

`gmpy2`

`2**log2(x)`

`x`

I can see how to directly develop a log, but not how to get back, eg, Taylor series needs a lot of terms... How can I write a power function myself? and @dan04 reply. Code follows.

`from gmpy2 import gcd, floor, next_prime, is_prime`

from gmpy2 import factorial, sqrt, exp, log,log2,log10,exp2,exp10

from gmpy2 import mpz, mpq, mpfr, mpc, f_mod, c_mod,lgamma

from time import clock

import random

from decimal import getcontext

x=getcontext().prec=1000 #also tried 56, 28

print(getcontext())

def rint():#check accuracy of exp(log(x))

e=exp(1)

l2=log(2)

l10=log(10)

#x=random.randint(10**20,10**21) --replaced with an actual value on next line

x=481945878080003762113

# logs to different bases

x2=log2(x)

x10=log10(x)

xe=log(x)

# logs back to base e

x2e=xe/l2

x10e=xe/l10

#

e2=round(2**x2)

e10=round(10**x10)

ex=round(e**xe)

#

ex2e=round(2**x2e)

ex10e=round(10**x10e)

error=5*x-(e2+e10+ex+ex2e+ex10e)

print(x,"error sum",error)

#print(x,x2,x10,xe)

#print(x2e,x10e)

print(e2,e10,ex)

print(ex2e,ex10e)

rint()

Answer

As long as you set the decimal module accuracy, the usual suggestion is to use Decimal datatype

```
from decimal import Decimal, getcontext
getcontext().prec = 1000
# Just a different method to get the random number:
x = Decimal(round(10**20 * (1 + 9 * random.random())))
x10 = Decimal.log10(x)
e10 = 10**x10
e10 - x
#outputs: Decimal('5.2E-978')
```

For different bases you may want to use the logarithmic formula:

```
x2 = Decimal.log10(x) / Decimal.log10(Decimal('2'))
e2 = 2**x2
e2 - x
#outputs: Decimal('3.9E-978')
```