mod | Modular arithmetic in Python :100 | Math library
kandi X-RAY | mod Summary
kandi X-RAY | mod Summary
Modular arithmetic in Python. Modular arithmetic is arithmetic for integers, where numbers wrap around when reaching a given value called modulus. For example 6 ≡ 1 (mod 5). Modular arithmetic has several practical applications including: music, banking, book publishing, cryptography... and of course math. The purpose of this package is to simplify the use of modular arithmetic in Python3.
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mod Examples and Code Snippets
from mod import Mod
# Funny math here
x = Mod(5, 7) # x ≡ 5 (mod 7)
(x + 2) == 0 # True: 5 + 2 ≡ 7 ≡ 0 (mod 7)
(x + 7) == x # True: 5 + 7 ≡ 12 ≡ 5 (mod 7)
(x**3) == (x + 1) # True: 5³ ≡ 125 ≡ 6 (mod 7)
(1 // x) == 3 # True:
def bin_exp_mod(a, n, b):
"""
>>> bin_exp_mod(3, 4, 5)
1
>>> bin_exp_mod(7, 13, 10)
7
"""
# mod b
assert not (b == 0), "This cannot accept modulo that is == 0"
if n == 0:
return 1
if
def find_mod_inverse(a: int, m: int) -> int:
if gcd(a, m) != 1:
raise ValueError(f"mod inverse of {a!r} and {m!r} does not exist")
u1, u2, u3 = 1, 0, a
v1, v2, v3 = 0, 1, m
while v3 != 0:
q = u3 // v3
v1, v2
Community Discussions
Trending Discussions on mod
QUESTION
I am a computer science student; I am studying the Algorithms course independently.
During the course, I saw this question:
Given an n-bit integer N, find a polynomial (in n) time algorithm that decides whether N is a power (that is, there are integers a and k > 1 so that a^k = N).
I thought of a first option that is exponential in n: For all k , 1
For example, if N = 27, I will start with k = 2 , because 2 doesn't divide 27, I will go to next k =3. I will divide 27 / 3 to get 9, and divide it again until I will get 1. This is not a good solution because it is exponential in n.
My second option is using Modular arithmetic, using ak ≡ 1 mod (k+1) if gcd(a, k+1 ) = 1 (Euler's theorem). I don't know if a and k are relatively prime.
I am trying to write an algorithm, but I am struggling to do it:
...ANSWER
Answered 2022-Mar-15 at 10:07Ignoring the cases when N is 0 or 1, you want to know if N is representable as a^b for a>1, b>1.
If you knew b, you could find a in O(log(N)) arithmetic operations (using binary search). Each arithmetic operation including exponentiation runs in polynomial time in log(N), so that would be polynomial too.
It's possible to bound b: it can be at most log_2(N)+1, otherwise a will be less than 2.
So simply try each b from 2 to floor(log_2(N)+1). Each try is polynomial in n (n ~= log_2(N)), and there's O(n) trials, so the resulting time is polynomial in n.
QUESTION
I am creating a custom video player, I would like to add a video preview when the user hovers a progress bar.
I am able to generate thumbnails using FFmpeg as follows.
...ANSWER
Answered 2022-Mar-27 at 18:50You will have to make your own tool for creating the WEBVTT file. And it's a simple process, you just need to get the information you need and fill it in the following format:
QUESTION
I don't have much experience in go but I have been tasked to execute a go project :)
So i need to build the go project and then execute it
Below is the error when i build the go project. Seems to be some dependency(package and io/fs) is missing
...ANSWER
Answered 2021-Aug-12 at 05:56This package requires go v1.16, please upgrade your go version or use the appropriate docker builder.
QUESTION
Using the cxx crate: https://crates.io/crates/cxx
I have the following struct on Rust:
...ANSWER
Answered 2022-Jan-27 at 20:47Try adding:
QUESTION
I have that PyCharm is halting on all my exceptions, even the ones I am handling in a try except
block. I do not want it to break there - I am handling and perhaps expecting an error. But every other exception I do want it to halt and suspend execution (e.g. so that I have the program state and debug it).
How does one do that?
I tried going into the python exception breakpoint option but I didn't see an option like "break only on unhandled exceptions" e.g as suggested by these:
- Stop PyCharm If Error
- https://intellij-support.jetbrains.com/hc/en-us/community/posts/206601165-How-to-enable-stopping-on-unhandled-exceptions-
note this is my current state, note how it stopped in my try block... :(
I tried:
...ANSWER
Answered 2022-Jan-25 at 23:49I think it is already working actually, but you are in fact not catching the correct error. In your code you have:
QUESTION
I've got this function here:
...ANSWER
Answered 2022-Jan-11 at 17:04OK, based on responses in IRC, this does not appear to be possible. One suggested workaround:
QUESTION
Can't find a way to get this to work:
sub triple(Str:D $mod where * ~~ any @modifiers = 'command' ) { }
If I don't pass in an argument, I get an error:
Too few positionals passed; expected 1 argument but got 0
With a question mark after $mod
:
sub triple(Str:D $mod? where * ~~ any @modifiers = 'command' ) { }
I get:
Constraint type check failed in binding to parameter '$mod'; expected anonymous constraint to be met but got Str (Str)
ANSWER
Answered 2022-Jan-10 at 22:45Looks like it may have been a precedence problem. This works:
QUESTION
The following code gets player data but each dataset is different. The first data it sees is the quarterback data, so it uses these columns for all the data going forward. How can I change the header so that for every different dataset it encounters, the correct headers are used with the correct data?
...ANSWER
Answered 2022-Jan-01 at 22:14Here is my attempt. A few things to note. I am not printing to CSV but just showing you the dataframes with the correct header information, you can handle the CSV output later.
You press enter after running the program to see the next tables with different headers.
QUESTION
I have the following code for connecting to a Postgres database:
...ANSWER
Answered 2021-Dec-21 at 21:47The issue is that when connecting in a docker-compose
network, you have to connect to the hostname of the container, in this case db
.
You could also use the other container's IP
but would take additional amount of work, it's simpler to just use the hostname.
In other words, you have the wrong connection string, I got this as well when connecting to localhost
QUESTION
I'm using godbolt to get assembly of the following program:
...ANSWER
Answered 2021-Dec-13 at 06:33You can see the cost of instructions on most mainstream architecture here and there. Based on that and assuming you use for example an Intel Skylake processor, you can see that one 32-bit imul
instruction can be computed per cycle but with a latency of 3 cycles. In the optimized code, 2 lea
instructions (which are very cheap) can be executed per cycle with a 1 cycle latency. The same thing apply for the sal
instruction (2 per cycle and 1 cycle of latency).
This means that the optimized version can be executed with only 2 cycle of latency while the first one takes 3 cycle of latency (not taking into account load/store instructions that are the same). Moreover, the second version can be better pipelined since the two instructions can be executed for two different input data in parallel thanks to a superscalar out-of-order execution. Note that two loads can be executed in parallel too although only one store can be executed in parallel per cycle. This means that the execution is bounded by the throughput of store instructions. Overall, only 1 value can only computed per cycle. AFAIK, recent Intel Icelake processors can do two stores in parallel like new AMD Ryzen processors. The second one is expected to be as fast or possibly faster on the chosen use-case (Intel Skylake processors). It should be significantly faster on very recent x86-64 processors.
Note that the lea
instruction is very fast because the multiply-add is done on a dedicated CPU unit (hard-wired shifters) and it only supports some specific constant for the multiplication (supported factors are 1, 2, 4 and 8, which mean that lea can be used to multiply an integer by the constants 2, 3, 4, 5, 8 and 9). This is why lea
is faster than imul
/mul
.
I can reproduce the slower execution with -O2
using GCC 11.2 (on Linux with a i5-9600KF processor).
The main source of source of slowdown comes from the higher number of micro-operations (uops) to be executed in the -O2
version certainly combined with the saturation of some execution ports certainly due to a bad micro-operation scheduling.
Here is the assembly of the loop with -Os
:
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