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POUsing GMP to calculate very large Integers from formulas
 

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  1. POUsing GMP to calculate very large Integers from formulas
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    <p>I was having a hard time to figure out how to deal with a problem I encountered. As a part of a complex formula, I need to calculate a part that quickly overflows double, i.e. results get up to ~ 1.59*10^(1331) (calculated with mathematica). Of course this is out of the range of double. Then I was thinking of using long double, which on my linux system with <code>gcc 4.6.3</code> is 16byte. </p> <p>1) double precision (8byte) has a possible range of up to 10^(308). Am I right in saying, that long double then increases the actual precision, but not the possible numeric range of values? I remember that I heard that it can be either or, depending on the system and the compiler. Is that true ? At least I still get NaN when I try to calculate my values with long double. </p> <p>2.) I was then looking for a way to actually calculate these results and I found the GNU <code>gmp</code>. I heard that you can represent very large integers and I thought this might help. However, reading the documentation, it seems that with </p> <pre><code> mpz_t x; mpz_init(x); mpz_set_*(x,#); </code></pre> <p>I can assign values to <code>gmp</code> integer data types, but in order to do that, I can "only" choose to assign values that can be represented by built-in data types like double or (u/s)int etc. All I found for how to assign really huge numbers was to use <code>mpz_set_str()</code> to assign the number from a string. How would I assign a number that is the result of a complex calculation ? Simply speaking, formulas look like this: </p> <pre><code>long double res1,res2=0.0; int a,b; a=780; b=741; float d,d1,o,s; // can be values in [0.01,100] res1=(2*(pow(b,2)*pow(E,b*(o + s))*(pow(d1,2) + pow(E,a*s)*(-1 + pow(E,a*o)) + pow(d,2)*(-1 + pow(E,a*s))) + pow(a,2)*pow(E,a*(o + s))*(pow(E,b*s)*(pow(E,b*o) + (-1 + d)*(1 + d + b*o)) + (-d + d1)*(d + d1 + b*o + b*d*s)) - a*b*(pow(d1,2)*(pow(E,a*(o + s)) + pow(E,b*(o + s))) + pow(E,a*o + (a + b)*s)*(-2 + 2*pow(E,b*o) - b*o) + d1*pow(E,a*s)*(-pow(E,b*o) + pow(E,a*o)*(1 + b*o)) + pow(d,2)*pow(E,a*s)*(-pow(E,b*o) + pow(E,b*(o + s)) + pow(E,a*o)*(-1 + pow(E,b*s) - b*s)) + d*(-(d1*pow(E,b*(o + s))) + (1 + d1)*pow(E,b*o + a*s) - pow(E,a*s + b*(o + s)) + pow(E,b*s + a*(o + s))*(1 + b*o) + pow(E,a*(o + s))*(-1 - b*o + b*d1*s)))))......; </code></pre> <p>res2 will also be of this kind, and in the end I need to calculate res1/res2, which usually becomes a very small number.</p> <p>I was thinking of splitting the formulas and adding terms to mpg_z in order to not get out of double range for each term, but as the formulas are so long and complex, that this is almost impossible. </p> <p>So in summary, the problem is, that my intermediate results can get so huge that no data type is capable of storing them, so I cannot assign it to mpz and get rid of this problem.</p> <p>I am aware that I want to calculate a double value and actually use mpz_t for integers. As far as I understand this is the only way to store such big data, since mpf_t can only handle float type. To be honest, there is still confusion on my side about the representation in <code>gmp</code>.</p> <p>Any ideas how to approach this ?</p>
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    1. USShafik Yaghmour
    1. UStheuni
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    1. COConsider using all mpz_t variables. Lose the integers variables (which are promoted to doubles in the part of your code that I can see), you gain nothing by using them anyway. Make everything mpz_t from the very start of your function. BTW what are you trying to do?
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      1. POUsing GMP to calculate very large Integers from formulas
      1. USjim mcnamara
    2. COIt looks like you're not doing integer arithmetic, so I'd stick with mpf_t and implement your whole formula using the floating arithmetic provided by gmp.
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      1. USmwv
    3. COThis is theoretical population genetics and I am trying to calculate moments of inter-coaescent times given an arbitrary demographic piecewise function
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      1. POUsing GMP to calculate very large Integers from formulas
      1. UStheuni
 

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