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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
Object model instruction 0x97 ldelem.i: Load the element with type native int at index onto the top of the stack as a native int. Object model instruction 0x90 ldelem.i1: Load the element with type int8 at index onto the top of the stack as an int32. Object model instruction 0x92 ldelem.i2
Scheme offer two functions, remainder and modulo – Ada and PL/I have mod and rem, while Fortran has mod and modulo; in each case, the former agrees in sign with the dividend, and the latter with the divisor. Common Lisp and Haskell also have mod and rem, but mod uses the sign of the divisor and rem uses the sign of the dividend.
If a ≡ b (mod m), then it is generally false that k a ≡ k b (mod m). However, the following is true: If c ≡ d (mod φ(m)), where φ is Euler's totient function, then a c ≡ a d (mod m) —provided that a is coprime with m. For cancellation of common terms, we have the following rules: If a + k ≡ b + k (mod m), where k is any integer ...
The congruence relation, modulo m, partitions the set of integers into m congruence classes. Operations of addition and multiplication can be defined on these m objects in the following way: To either add or multiply two congruence classes, first pick a representative (in any way) from each class, then perform the usual operation for integers on the two representatives and finally take the ...
The basic reduction step divides the product into two e-bit parts, multiplies the high part by d, and adds them: (ax mod 2 e) + d ⌊ ax/2 e ⌋. This can be followed by subtracting m until the result is in range. The number of subtractions is limited to ad/m, which can be easily limited to one if d is small and a < m/d is chosen.
The random energy model (REM) is one of the simplest models of statistical mechanics of disordered systems, and probably the simplest model to show the meaning and power of the replica trick to the level 1 of replica symmetry breaking. The model is especially suitable for this introduction because an exact result by a different procedure is ...
c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m). Modular exponentiation is efficient to compute, even for very large integers. On the other hand, computing the modular discrete logarithm – that is, finding the exponent e when given b , c , and m – is believed to be difficult.