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Binary Exponentiation | Numerical Recipes

https://numericalrecipes.wordpress.com/2009/06/05/binary-exponentiation

Just another WordPress.com weblog. The code examples in this post are also available here. Although I have already written something on binary exponentiation, as it applied to modular exponentiation. For an n-th power to exist, the object being exponentiated must fulfill certain conditions, which can basically be summarized in belonging to a more general set that has a well-behaved multiplication operation defined. Good behavior can be translated into closure. And even to a ring. Class, and write a.

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Post Index | Numerical Recipes

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Just another WordPress.com weblog. Prime Numbers and Factorization. The Sieve of Erathostenes. Modular Multiplicative Inverse (Extended Euclidean Algorithm). Greatest Common Divisor (Euclidean Algorithm). Cooley-Tukey’s radix 2 FFT with Decimation in Time. The Cooley-Tukey FFT Algorithm for General Factorizations. Leave a Reply Cancel reply. Enter your comment here. Fill in your details below or click an icon to log in:. Address never made public). Notify me of new comments via email. Back from the Dead.

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Back from the Dead | Numerical Recipes

https://numericalrecipes.wordpress.com/2010/09/09/back-from-the-dead

Just another WordPress.com weblog. Back from the Dead. The previous post in this blog is more than nine months old, and before that it already had been inactive for six more. There have been good reasons for that long silence. Chiefly, the birth of Gabriela, our second child, in November 2009. Well, all that is about to change! Business as usual will resume shortly with a post on Fibonacci numbers. And there’s also stuff in the making regarding the Chinese remainder theorem. Feed You can leave a response.

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The Cooley-Tukey FFT Algorithm for General Factorizations | Numerical Recipes

https://numericalrecipes.wordpress.com/2009/05/29/the-cooley-tukey-fft-algorithm-for-general-factorizations

Just another WordPress.com weblog. The Cooley-Tukey FFT Algorithm for General Factorizations. All code examples in the post have been included in the nrp base.py. Module, which can be downloaded from this repository. As presented in the previous post. Cooley-Tukey’s FFT algorithm. Say that N = P Q. Following the previous approach, we could try to split the calculation of the DFT into Q DFTs of size P, by rewriting it as. Where the inner summation has been reduced to a standard DFT of size P. Furtherm...

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Modular Exponentiation | Numerical Recipes

https://numericalrecipes.wordpress.com/2009/03/20/modular-exponentiation

Just another WordPress.com weblog. I have a post cooking on wheel factorization. What we are after is determining a. Mod m), or to put it in plain English, the remainder of a to the power of b, divided by m. Doesn’t seem much, does it? We could just go ahead and write:. Def modExp1(a, b, m) : Computes a to the power b, modulo m, directly return a* b % m. We can, and will, use modular arithmetic. Def modExp2(a, b, m) : Computes a to the power b, modulo m, a little less directly return (a%m)* b % m. The on...

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Coming Soon… | Numerical Recipes

https://numericalrecipes.wordpress.com/coming-soon

Just another WordPress.com weblog. This page is a place holder for things that I would like to see find their way into the blog. It is also the right place to leave comments proposing new topics, or asking for something in the pipeline to be pushed forward…. Fast computation of large Fibonacci numbers. Some factorization algorithm not included in the. Factorization in the Dark Ages. The Chinese Remainder Theorem. Cooley-Tukey’s algorithm for general factorizations. Prime factor FFT algorithm. Build a web...

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Good boy! | Numerical Recipes

https://numericalrecipes.wordpress.com/2009/11/30/good-boy

Just another WordPress.com weblog. Just a quick pat on my own shoulder…. Posted this very last weekend, was proposed by yours truly:. The divisors of 12 are: 1,2,3,4,6 and 12. The largest divisor of 12 that does not exceed the square root of 12 is 3. We shall call the largest divisor of an integer n that does not exceed the square root of n the pseudo square root (PSR) of n. It can be seen that PSR(3102)=47. Let p be the product of the primes below 190. Find PSR(p) mod 10. And daniel.is.fischer. With all...

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The Discrete Fourier Transform | Numerical Recipes

https://numericalrecipes.wordpress.com/2009/04/30/the-discrete-fourier-transform

Just another WordPress.com weblog. The Discrete Fourier Transform. I’m currently a little fed up with number theory. So its time to change topics completely. Specially since the post on basic integer factorization. Completes what I believe is a sufficient toolkit to tackle a very cool subject: the fast Fourier transform (FFT). The Discrete Fourier Transform. Without further explanation, we will begin by writing down the analytical expression of the DFT,. And of its corresponding inverse transform,. It is...