Best way to handle the ratio which cannot be represented as floating point numbers. I need to calculate the ratio of the form: s=sum_1^3 q_i p_i=(q_i)/(sum_1^3q_i} where q_i >0. One problem is that q_i are too small that they can not represented as floating point numbers, then I can try logarithms z_i=log(q_i) and log(pi)=log(q_i)−log(q_1+q_2+q_3), at this moment, I know log(q_1)=−2012,log(q_2)=−2013,log(q_3)=−2014, but how to deal with log(q_1+q_2+q_3), any one could give me some idea?

ohgodamnitw0 2022-09-06 Answered
Best way to handle the ratio which cannot be represented as floating point numbers.
I need to calculate the ratio of the form:
s = 1 3 q i , p i = q i 1 3 q i
where q i > 0. One problem is that q i are too small that they can not represented as floating point numbers, then I can try logarithms z i = l o g ( q i ) and l o g ( p i ) = l o g ( q i ) l o g ( q 1 + q 2 + q 3 ), at this moment, I know l o g ( q 1 ) = 2012 , l o g ( q 2 ) = 2013 , l o g ( q 3 ) = 2014, but how to deal with l o g ( q 1 + q 2 + q 3 ), any one could give me some idea?
thanks
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Answers (1)

goffaerothMotw1
Answered 2022-09-07 Author has 10 answers
Hint
Let me suppose q 1 > q 2 > q 3 . So,
p 1 = q 1 q 1 + q 2 + q 3 = 1 1 + q 2 q 1 + q 3 q 1
Now,
p 2 = p 1 q 2 q 1
p 3 = p 2 q 3 q 2
I suppose that this will give you your number for almost any accuracy (computing the required ratios from the logarithms).
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