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For the purposes of these tables, a, b, and c represent valid values (literals, values from variables, or return value), object names, or lvalues, as appropriate. R, S and T stand for any type(s), and K for a class type or enumerated type. Some of the operators have alternative spellings using digraphs and trigraphs or operator synonyms.
The Barrett multiplication previously described requires a constant operand b to pre-compute [] ahead of time. Otherwise, the operation is not efficient. Otherwise, the operation is not efficient. It is common to use Montgomery multiplication when both operands are non-constant as it has better performance.
replacing integer multiplication by a constant with a combination of shifts, adds or subtracts; replacing integer division by a constant with a multiplication, taking advantage of the limited range of machine integers. [3] This method also works if divisor is a non-integer sufficiently greater than 1, e.g. √2 or π. [4]
larger of two floating-point values fmin: smaller of two floating-point values fdim: positive difference of two floating-point values nan nanf nanl: returns a NaN (not-a-number) Exponential functions exp: returns e raised to the given power exp2: returns 2 raised to the given power expm1: returns e raised to the given power, minus one log
The algorithm first finds the largest value among the n i and then the supremum within the set of { n i \ i ≠ M}. Then it raises x M to the power q, multiplies this value with x N, and then assigns x N the result of this computation and n M the value n M modulo n N.
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A character in single quotes (example: 'R'), called a "character constant," represents the value of that character in the execution character set, with type int. Except for character constants, the type of an integer constant is determined by the width required to represent the specified value, but is always at least as wide as int .
However, this example cheats, in that the value of n is not itself limited to a single digit. This has the consequence that the method will fail for n > 3200 or so. In a more general implementation, n would also use a multi-digit representation.