On 1 sep, 11:08, Robert Bradshaw <[email protected]> wrote:
> On Aug 29, 2009, at 11:05 PM, Rolandb wrote:
>
> > Hi,
>
> > Using math.log has a disadvantage; it is less accurate.
>
> > sage: print n(math.log(2),100)
> > sage: print n(log(2),100)
> > 0.69314718055994528622676398300
> > 0.69314718055994530941723212146
>
> Yes, it is. Accuracy vs. speed is a common tradeoff one needs to make.
>
> If you're going for a numerical answer, log(2).n(1000) will give you
> 1000 bits of precision. Adjust as you see fit for your application.
>
> - Robert
Hi Robert,
I tested several solutions and I found that there is a much better
approach.
def expon1(mx,g): return int(ln(mx)/ln(g))+1
def expon2(mx,g): return floor(log(mx)/log(g))+1
def expon3(mx,g): return floor(ln(mx)/ln(g))+1
def expon4(mx,g): return floor(math.log(mx)/math.log(g))+1
def expon5(mx,g): return floor(n(log(mx),100)/n(log(g),100))+1
def expon6(mx,g):
if g>mx: return 1
k=0
m=g
while m*g<=mx:
m=m*g
k+=1
return k+2
1. 625 loops, best of 3: 1.15 ms per loop
2. 625 loops, best of 3: 998 µs per loop
3. 625 loops, best of 3: 993 µs per loop
4. 625 loops, best of 3: 6.77 µs per loop
5. 625 loops, best of 3: 696 µs per loop
6. 625 loops, best of 3: 7.71 µs per loop
Roland
The last method is best, although I didn't expected it to be.
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