FOUNDATION SERVICES - Manipulating numbers without arithmetic

Manipulating numbers without arithmetic

A few carefully chosen test cases can be worth thousands of random tries. The system provides functions to fine-tune floating-point values portably. NextAfter, which returns the floating-point neighbor of its first argument in the direction of its second, produces values adjacent to the seam of the approximation:

  void ArtfulTest(int testCount) {
      const double kSeam = 0x1.0p-27;
      double xDown = kSeam, xUp = kSeam;
      for (int i = 0; i < testCount; i++) {
          xDown = NextAfter(xDown, -kInfinity);
          ArcTanhTest(xDown); // compare Sample... with SlowButSure...
          xUp = NextAfter(xUp, +kInfinity);
          ArcTanhTest(xUp);
      }
  }

Other functions help decompose a floating-point value into its exponent and significand without resorting to nonportable integer operations that depend on intimate details of the data formats. Here is a typical sequence applied to a double number:

  double signSaver = CopySign(1.0, value);
  value = Abs(value); // synonymous with CopySign(value, 1.0)
  double powerOfTwo = Logb(value);
  double significand = Scalb(value, (long) -powerOfTwo);

After this sequence, the following formula holds exactly for a finite, nonzero value:

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