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The Java language allows platforms to use available floating-point hardware that can provide extended floating-point support with exponents that contain more bits than the standard Java primitive type double (in the absence of the strictfp modifier). Consequently, these platforms can represent a superset of the values that can be represented by the standard floating-point types. Floating-point computations on such platforms can produce different results than would be obtained if the floating-point computations were restricted to the standard representations of float and double. According to the JLS, §15§15.4, "FP-strict Expressions" [JLS 2005]:

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The JVM may choose to treat this case as FP-strict; if it does so, overflow occurs. Because the expression is not FP-strict, an implementation may use an extended exponent range to represent intermediate results.

class Example {
  public static void main(String[] args) {
    double d = Double.MAX_VALUE;
    System.out.println("This value \"" + ((d * 1.1) / 1.1) + "\" cannot be represented as double.");
  }
}

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For maximum portability, use the strictfp modifier within an expression (class, method, or interface) to guarantee that intermediate results do not vary because of implementation-defined behavior. The calculation in this compliant solution is guaranteed to produce infinity because of the intermediate overflow condition, regardless of what floating-point support is provided by the platform.

strictfp class Example {
  public static void main(String[] args) {
    double d = Double.MAX_VALUE;
    System.out.println("This value \"" + ((d * 1.1) / 1.1) + "\" cannot be represented as double.");
  }
}

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Native floating-point hardware provides greater range than double. On these platforms, the JIT is permitted to use floating-point registers to hold values of type float or type double (in the absence of the strictfp modifier), even though the registers support values with greater exponent range than that of the primitive types. Consequently, conversion from float to double can cause an effective loss of magnitude.

class Example {
  double d = 0.0;

  public void example() {
    float f = Float.MAX_VALUE;
    float g = Float.MAX_VALUE;
    this.d = f * g;
    System.out.println("d (" + this.d + ") might not be equal to " +
                       (f * g));
  }

  public static void main(String[] args) {
    Example ex = new Example();
    ex.example();
  }
}

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This compliant solution uses the strictfp keyword to require exact conformance with standard Java floating-point. Consequently, the intermediate value of both computations of f * g is identical to the value stored in this.d, even on platforms that support extended range exponents.

strictfp class Example {
  double d = 0.0;

  public void example() {
    float f = Float.MAX_VALUE;
    float g = Float.MAX_VALUE;
    this.d = f * g;
    System.out.println("d (" + this.d + ") might not be equal to " +
                       (f * g));
  }

  public static void main(String[] args) {
    Example ex = new Example();
    ex.example();
  }
}

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NUM05-J. Do not use denormalized numbers      03. Numeric Types and Operations (NUM)