The Chudnovsky formula is a power series: Each new term in the partial sum adds a fixed number of digits of accuracy. Produces the 8-digit floating-point value 3.1415929 On the other hand, the statement vpa(p,8) Which is an attractive alternative to the familiar 22/7. Produces three terms in the continued fraction approximation of π p = 3 + 1/(7 + 1/16) For example, the MATLAB statement p = rat(pi)
The vpa function initiates variable-precision floating-point arithmetic: Arithmetic quantities are represented by decimal fractions of a specified length together with a power-of-10 exponent.Īrithmetic operations, including divisions and roots, can involve roundoff errors at the level of the specified accuracy. Quotients and roots are not computed unless the result is an exact integer. Integer length increases as necessary, limited only by computer time and storage requirements. The sym function initiates exact rational arithmetic: Arithmetic quantities are represented by quotients and roots of large integers. Symbolic Math Toolbox provides two styles of high-precision arithmetic: sym and vpa. The machine that he built for this project (Figure 2) has two Intel ® Xeon ® processors with a total of 12 cores, 96 gigabytes of RAM, and 20 external hard disks with a combined capacity of 32 terabytes. Kondo is a systems engineer who assembles personal computers at his home in Japan. His computing software, “y-cruncher,” began as a class project at Palo Alto High School. Yee is now a graduate student at the University of Illinois. Their computation took 90 days on a “homebrew” PC. Last August, two computer hobbyists, Alexander Yee and Shigeru Kondo, announced that they had set a world record by computing 5 trillion digits of π (Figure 1). MATLAB ® implementations of the most widely used algorithms for computing π illustrate two different styles of arithmetic available in Symbolic Math Toolbox ™: exact rational arithmetic and variable-precision floating-point arithmetic. Computing hundreds, or trillions, of digits of π has long been used to stress hardware, validate software, and establish bragging rights.
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