Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of π calculation

More than 200 million decimal places of π were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R.P. Brent in 1976. Correctness of the calculation was verified through Borwein´s quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer. Two programs generated values up to 3×2²⁶, about 201 million. The two results agreed except for the last 21 digits. The results also agree with the 133,554,000-place calculation of π that was done by the author in January 1987. Compared to the record in 1987, 50% more decimal digits were calculated with about 1/6 of CPU time. The computation was performed with a real-arithmetic-based vectorized fast Fourier transform (FFT) multiplier and vectorized multiple-precision add, subtract, and (single-word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820