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The % operator in Dart is the arithmetic modulo operator, which calculates the Euclidean remainder of a division operation between two numbers. Unlike the modulo operator in many C-style languages (which perform a truncating remainder), Dart’s % operator strictly enforces Euclidean division, guaranteeing that the returned remainder is always non-negative regardless of the operands’ signs. 
num result = dividend % divisor;

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Type Evaluation

The static and runtime return type of the % operation is determined by the types of its operands:
  • If both operands are of type int, the operation yields an int.
  • If at least one operand is of type double, the operation yields a double.
int intResult = 10 % 3;         // Evaluates to 1
double doubleResult = 10.5 % 3; // Evaluates to 1.5

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Euclidean Modulo Behavior

Dart calculates the modulo such that the result r always satisfies the mathematical condition 0 <= r < |divisor|. Because it is a Euclidean modulo, negative operands will not produce a negative remainder. 
// Standard positive operands
print(5 % 3);   // Evaluates to 2

// Negative dividend
print(-5 % 3);  // Evaluates to 1 (Contrast with C++/Java which yield -2)

// Negative divisor
print(5 % -3);  // Evaluates to 2

// Negative dividend and divisor
print(-5 % -3); // Evaluates to 1
Note: If you require a truncating remainder operation where the result retains the sign of the dividend, Dart provides the num.remainder() method as the strict alternative to the % operator.

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Exceptional Cases

The behavior of the % operator when the divisor is zero diverges based on the operand types:
  • Integer Division by Zero: Evaluating int % 0 throws an UnsupportedError (Integer division by zero).
  • Floating-Point Division by Zero: Evaluating double % 0 or num % 0.0 does not throw. Instead, it evaluates to NaN (Not a Number) in compliance with IEEE 754 floating-point standards.
int a = 5 % 0;       // Throws UnsupportedError
double b = 5.0 % 0;  // Evaluates to NaN
double c = 5 % 0.0;  // Evaluates to NaN
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