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Optimizing Lagged Fibonacci Generators for Large-Scale Computations
Lagged Fibonacci Generators (LFGs) are powerful tools for generating pseudo-random sequences in simulations and cryptography. While traditional implementations become inefficient when computing sparse terms at large indices, this blog explores an optimized approach using matrix exponentiation and modular arithmetic. By encoding the recurrence relation in a transformation matrix and leveraging GPU acceleration, the method achieves scalability and speed, making it ideal for large-scale applications.
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Some Interesting Properties of the Exclusive Or (XOR)
The exclusive-OR — also known as exclusive disjunction (short: XOR) or antivalence — is a Boolean operation that outputs true only when exactly one of its two inputs is true (i.e., when the inputs differ). XOR has numerous applications, including cryptography, Gray codes, parity checks, and CRC checks, among others. In this blog post, we will explore some of its interesting properties that can be useful in practice.
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Efficient Computation of Sparse Fibonacci Subsequences
The Fibonacci sequence is a cornerstone of mathematics, defined by its elegant recurrence relation. While traditionally computed iteratively or recursively, obtaining specific terms like the 1000th or 2000th number seems to require calculating all preceding terms. But is this really necessary? In this post, we explore a powerful technique to compute arbitrary Fibonacci terms directly — bypassing the need for sequential computation. We’ll also tackle an exciting challenge: efficiently finding one thousand Fibonacci numbers modulo a given value, corresponding to every 10th prime greater than a trillion.
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Don't Drink and Derive: A Simple Proof that 1 = 2
In this blog post, we present a fun little proof that 1 is actually equal to 2. Or is it?
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CUDA Basics: Decoding DTMF Signals
Discover the fundamentals of CUDA programming through a dual-tone multi-frequency (DTMF) signaling example. Learn how to generate DTMF signals, save them as .wav files, design FIR bandpass filters, and decode dialed keys. This project includes a CUDA/C++ implementation (dtmfCuda.cu) to showcase the power of parallel computing for signal processing.