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3
votes
1answer
93 views

Compute hypergeometric function ratio: $\frac{_{2}F_{1}(a+1,b;c;x)}{_{2}F_{1}(a,b;c;x)}$?

I need a numerically stable way to compute the following ratio: $$\frac{_{2}F_{1}(a+1,b;c;x)}{_{2}F_{1}(a,b;c;x)}$$ All the parameters are real numbers, with $a< 0$,$\ $ $b,c > 0$ and ...
0
votes
1answer
50 views

How many years it would take our laptops to be as fast as the fastest super computer in 2000 [closed]

How many years it would take our laptops to be as fast as the fastest super computer in 2000 according to Moore's law?
3
votes
1answer
111 views

Fibonacci, variation on the theme

I am trying to calculate the numbers $n$ for which the $n$-th Fibonacci number $F_n$ is a multiple of $n$; that is fib(n)%n==0. Here is the best PARI code I could come up with (for the counting ...
2
votes
1answer
655 views

range of positive mantissa in given floating-point number representation

I am a student and I came to this question while solving problems regarding the float-points. ...
5
votes
2answers
100 views

How many bits to unambiguously represent fixed-point division?

Suppose I have a function which divides an $m$-bit unsigned integer $a$ by an $n$-bit unsigned integer $b$ and returns the quotient as a fixed-point number with $t$ fractional bits, truncating towards ...
2
votes
2answers
87 views

Integer arithmetic support on future HPC systems

I writing some robust geometric algorithms using quantization + integer arithmetic for evaluating exact predicates. However, since BlueGene's integer support is so terrible, it occurred to me that ...
3
votes
2answers
424 views

Need for quad precision in scientific computing?

Even if quad precision is not directly supported by most CPUs, many Compilers (GNU, Intel) support them. Also some software packages allow to compile with quad precision, e.g. PETSc. But is there ...
4
votes
2answers
130 views

Krylov subspace iterative methods in floating point arithmetic

Is there any work that considers Krylov subspace iterative methods in floating point arithmetic? I'm especially interested in how rounding errors influence the convergence and the accuracy of the ...
13
votes
4answers
310 views

In floating point arithmetic, why does numerical imprecision result from adding a small term to a difference of large terms?

I have been reading the book Computer Simulation of Liquids by Allen and Tildesley. Starting on page 71, the authors discuss the various algorithms that are used to integrate Newton's equations of ...
8
votes
3answers
317 views

Which is computed faster, $a^b$, $\log_a c$ or $\sqrt[b]{c}$?

Which is computed faster, $a^b$ or $\log_a c$ or $\sqrt[b]{c}$? $a$, $b$ and $c$ are positive reals with $b>1$. What kinds of algorithms will you use in the comparison? What are their ...
29
votes
2answers
2k views

Why is division so much more complex than other arithmetic operations?

I recently encountered a case where I needed an integer division operation on a chip that lacked one (ARM Cortex-A8). While trying to research why that must be, I found out that in general division ...