As pointed out by other answers, in python they return floats probably because of historical reasons to prevent overflow problems. However, they return integers in python 3. >>> import math >>> type(math.floor(3.1)) <class ‘int’> >>> type(math.ceil(3.1)) <class ‘int’> You can find more information in PEP 3141.
@Dave was the first to post an answer to this (with working code), and his answer has been an invaluable source of shameless copy and pasting inspiration to me. This post began as an attempt to explain and refine @Dave’s answer, but it has since evolved into an answer of its own. My method is … Read more
Initialize an array of 1001 integers with the values 0-1000 and set a variable, max, to the current max index of the array (starting with 1000). Pick a random number, r, between 0 and max, swap the number at the position r with the number at position max and return the number now at position … Read more
You can use negative numbers to round integers: >>> round(1234, -3) 1000.0 Thus if you need only most significant digit: >>> from math import log10, floor >>> def round_to_1(x): … return round(x, -int(floor(log10(abs(x))))) … >>> round_to_1(0.0232) 0.02 >>> round_to_1(1234243) 1000000.0 >>> round_to_1(13) 10.0 >>> round_to_1(4) 4.0 >>> round_to_1(19) 20.0 You’ll probably have to take care … Read more
Here’s the best algorithm I know of (in Python) def prime_factors(n): “””Returns all the prime factors of a positive integer””” factors = [] d = 2 while n > 1: while n % d == 0: factors.append(d) n /= d d = d + 1 return factors pfs = prime_factors(1000) largest_prime_factor = max(pfs) # The … Read more
Or you could use the modulo operator: (d % 1) == 0
-ffast-math does a lot more than just break strict IEEE compliance. First of all, of course, it does break strict IEEE compliance, allowing e.g. the reordering of instructions to something which is mathematically the same (ideally) but not exactly the same in floating point. Second, it disables setting errno after single-instruction math functions, which means … Read more
Finite Projective Geometries The axioms of projective (plane) geometry are slightly different than the Euclidean geometry: Every two points have exactly one line that passes through them (this is the same). Every two lines meet in exactly one point (this is a bit different from Euclid). Now, add “finite” into the soup and you have … Read more
The main trick behind this algorithm is that if you, observing a stream of random integers, see an integer which binary representation starts with some known prefix, there is a higher chance that the cardinality of the stream is 2^(size of the prefix). That is, in a random stream of integers, ~50% of the numbers … Read more
np.max is just an alias for np.amax. This function only works on a single input array and finds the value of maximum element in that entire array (returning a scalar). Alternatively, it takes an axis argument and will find the maximum value along an axis of the input array (returning a new array). >>> a … Read more