(Start at the beginning of the series if you want more context.) Calculus operations It’s relatively simple to do differentiation and integration of power series, since they’re just regular polynomial-style. No trigonometric identities, logarithms or other tricky integrals here. Just the plain rule for positive powers of x. For differentiation, we have: [latex]\frac{d}{dx}kx^{n} = knx^{n-1}[/latex]… Continue reading Exercising Ranges (part 7)

# Category: C++

## Exercising Ranges (part 6)

(Start at the beginning of the series if you want more context.) Multiplying power series Now we come to something that took considerable thought: how to multiply ranges. Doug McIlroy’s Haskell version of range multiplication is succinct, lazily evaluated and recursive. (f:ft) * gs@(g:gt) = f*g : ft*gs + series(f)*gt Which is to say, mathematically,… Continue reading Exercising Ranges (part 6)

## Exercising Ranges (part 5)

(Start at the beginning of the series if you want more context.) Generalising iota To pretty-print a reversible polynomial, we need to provide for reversibility of iota. So what is iota? It makes a range by repeatedly incrementing a value. What if instead of increment, we use an arbitrary function? We could do this with… Continue reading Exercising Ranges (part 5)

## Exercising Ranges (part 4)

(Start at the beginning of the series if you want more context.) On reversibility It occurs to me that I’ve been touting reversibility as a good thing, both implicitly and explicitly (for polynomials), and the reason for that is not just that I might want to print polynomials in natural decreasing-power-of-x order. The first reason… Continue reading Exercising Ranges (part 4)

## Exercising Ranges (part 3)

(Start at the beginning of the series if you want more context.) So, I was going to implement monoidal_zip, and to do that, I would clone zip_with.hpp. So I did that. Eric’s a great library author, and the ranges code is pretty easy to read. For the most part I found it concise, well-expressed and… Continue reading Exercising Ranges (part 3)

## Exercising Ranges (part 2)

(Start at the beginning of the series if you want more context.) First steps with power series A power series (or polynomial, to give it a more familiar term in the case where it’s finite) is represented simply as a sequence of coefficients of increasing powers of x. This is simple – to represent: [latex]1… Continue reading Exercising Ranges (part 2)

## Exercising Ranges (part 1)

The idea For some time since attending C++Now, I have been meaning to get around to playing with Eric Niebler’s range library. Eric presented ranges in a worked example as one of the keynotes at C++Now – a prior version of the talk that he gave at the Northwest C++ Users Group is currently available… Continue reading Exercising Ranges (part 1)

## “The Lambda Trick”

I just got back from C++Now, an excellent conference where C++ template metaprogramming experts abound. A phrase I overheard often was “the lambda trick”. It’s a trick for speeding up compiles when templates get deep. Every C++ programmer knows that deep templates can slow down compilation. Most assume that this is because of excessive code… Continue reading “The Lambda Trick”

## Recursive lambdas

One can assign a lambda to auto or to std::function. Normally one would assign a lambda to auto to avoid possible unwanted allocation from std::function. But if you want recursion, you need to be able to refer to the lambda variable inside the lambda, and you can’t do that if it’s assigned to auto. So… Continue reading Recursive lambdas

## Rules for using <random>

These days, it’s easy to do the right thing. Don’t do this: Don’t use std::rand(). Ever. Don’t use std::random_shuffle() to permute containers. (Too easy to misuse; can use std::rand() under the hood.) Don’t use any kind of clock for a seed. Don’t use mod (%) to get a random value into a range. It introduces… Continue reading Rules for using <random>