Itanium® Architecture for Programmers: Understanding 64-Bit Processors and EPIC Principles

8.9. APPROXPI: Using Floating-Point Instructions

The transcendental number π can be computed using many techniques. One method, which we do not hold up as the best, has its basis in the recognition that the area of a circle of radius a is πa² while the area of a square just large enough to enclose the circle is 4a² (see Figure 8-3). The ratio of the area of the circle to the area of the square is πa²/4a² or π/4. If we could separately measure the areas of the circle and the square, we could estimate π to be 4 times the ratio of the area of the circle to the area of the square.

Figure 8-3. Circle and enclosing square for estimating π

Consider a ...