hpr1292 :: Doomsday Remainders
Reflections on remainders inspired by Doomsday Rule sign-off. Applications to programming and arithm
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arithmetic, remainder, mod.
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Last Episode on Conway's Doomsday Rule ends with teaser on MOD(), a
"remainder" function defined for integer values (whole numbers):
MOD(K, m) = remainder when K is divided by "modulus" m.
Examples:
a. MOD(207, 7) = MOD(207 - 140, 7) = MOD(67, 7) = 4
b. MOD(1234567, 2) = 1 because the number is odd
MOD() function found in most spreadsheet programs, but it also shows up
as an operator in some programming languages: (a % b), or (a mod b).
Other functions referenced:
DIV(K, m) = quotient in integer division
where K = m * quotient + remainder (not returned)
0 <= remainder < m
DIVMOD(K, m) = (quotient, remainder) when K is divided by m
where remainder = MOD(K, m)
quotient = DIV(K, m)
K = m * quotient + remainder
Full Show Notes
https://hackerpublicradio.org/eps/hpr1292.txt
Links
- https://en.wikipedia.org/wiki/Modular_arithmetic
- https://www.khanacademy.org/math/applied-math/cryptography/modarithmetic/a/what-is-modular-arithmetic
- https://betterexplained.com/articles/fun-with-modular-arithmetic/
- https://mathworld.wolfram.com/Congruence.html
- https://en.wikipedia.org/wiki/ALGOL_60
- https://www.conservapedia.com/Pascal_%28programming_language%29
- https://www.gnu.org/software/libc/manual/html_node/Integer-Division.html#Integer-Division
- https://www.haskell.org/tutorial/numbers.html
- https://www.standardml.org/Basis/integer.html
- https://docs.python.org/2/library/functions.html#divmod
- https://docs.python.org/3/library/functions.html#divmod
- https://ruby-doc.org/core-2.0/Numeric.html
- https://en.wikipedia.org/wiki/Doomsday_rule
- https://en.wikipedia.org/wiki/Modulus_operation
- https://zetcode.com/lang/python/lists/
- https://docs.python.org/2/tutorial/introduction.html