Check this out (javascript):
function permute1(x) {
if (x.length == 1) return x;
let even = [];
let odd = [];
for (let i = 0; i < x.length; i += 2) {
even[i / 2] = x[i];
odd[i / 2] = x[i + 1];
}
return [].concat(permute1(even), permute1(odd));
}
function permute2(x, offset, stride) {
if (!offset) offset = 0;
if (!stride) stride = 1;
if (stride >= x.length) return [x[offset]];
return [].concat(permute2(x, offset, stride * 2), permute2(x, offset + stride, stride * 2));
}
function permute3(x) {
let result = [];
for (let i = 0; i < x.length; i++) {
let k = i;
// pretend 32-bit ints
k = ((k >> 1) & 0x55555555) | ((k & 0x55555555) << 1);
k = ((k >> 2) & 0x33333333) | ((k & 0x33333333) << 2);
k = ((k >> 4) & 0x0F0F0F0F) | ((k & 0x0F0F0F0F) << 4);
k = ((k >> 8) & 0x00FF00FF) | ((k & 0x00FF00FF) << 8);
k = ( k >> 16 ) | ( k << 16);
k = k >> (64 - Math.log2(x.length));
if (k < 0) k += x.length; // fix up due to signed ints
result[i] = x[k];
}
return result;
}
For arrays with power of two sizes, these perform the same permutation (but fail differently for non power of two sizes). Note that, with permute1, we effectively iterate over the entire input log2(n) times, so this is an O(nlogn) algorithm!edit: also, i think i may have misunderstood the relationship between your js version and your lambdatalk version. They seem to be the same to me?
Yes there is a relationship between the JS version and its translation into lambdatalk. My project is to replace the array based version by a list based version so that I can replace in this page http://lambdaway.free.fr/lambdaspeech/?view=PLR the inefficient unary numeration based implementation of numbers (using standard Church numbers or just lists) by a decimal position numeration. Standard multiplication of words seen as polynoms being O(n^2) I need to go further and implement fast multiplication. So my interest in FFT.
As you could see in http://lambdaway.free.fr/lambdaspeech/meca/JS.js, the lambdatalk's interpreter is a regular expression window running on the code (not an AST) and replacing in situ expressions by their values. A kind of Turing machine. I like the idea of overcoming limits of JS numbers using nothing but words and simple substitutions on words.