Modular multiplicative inverse [FINALIZED]

−0

Now posted: Print virtual fractions / 2-adic fractions / Modular multiplicative inverse

TL;DR

Print this values (or an extension of them):

Explanation

Virtual fractions are integers that have the feature that you can multiply them with the denominator and you get the numerator when you store them in a N-Bit integer.

For example, you have the 16 bit unsigned integer with the value 0xAAAB (43691). You can multiply it with 3 and get 1.

  3 * 0xAAAB  =  3 * 0b1010 1010 1010 1011  =  3 * 43691
  =  0x20001  =   0b10 0000 0000 0000 0001  =     131073
Storing it in a 16 bit variable drops the 1 at bit 17:
  =   0x0001  =      0b0000 0000 0000 0001  =          1

Or $3 \cdot 43691 = 1 \mod 65536$

This is basically a p-adic/2-adic number with a limited amount of digits. And it is the same as the modular multiplicative inverse with a modulus of 65536 ($2^{16}$).

This works only with bases that are odd, without any shifting. For this challenge we only print the ones with a numerator of 1.

Rules

Print at least 16 bit of the virtual fraction, you can use more.
Print at least the virtual fractions of 1/a for odd a where a<98.
You can print it in any normal base
You can print additional stuff, but it should be clear what parts belong to the virtual fractions and what not.
Your program should print the required output in less than 1h on a modern PC.

Ungolfed example

#!/usr/bin/env python3

import sys 

#Calculates the modular multiplicative inverse
def imod(a, n):
  c=1
  while c % a:
    c+=n
  return c//a

#Print the virtual fractions for 16-bit integers
n=2**16
for i in range(1,98,2): #For the values 1/1, 1/3, ... 1/97
  b = imod(i,n)
  print("{:>2} * 0x{:>04X} = {:2>} mod 0x{:>04X}".format(i,b,i*b%n,n))

code-golf finalized

posted 11 months ago

CC BY-SA 4.0

11mo ago by trichoplax‭

H_H‭

110 reputation 6 6 11 52

Raw

Markdown

History

Communities