RealPi Benchmark

RealPi provides some of the best and most interesting Pi calculation algorithms out there. This app is a benchmark which tests your Android device's CPU and memory performance. It calculates the value of Pi to many decimal places, unlike certain fake Pi benchmarks on the Android market.

You can also search for patterns in the resulting digits to find your birthday in Pi or find famous digit sequences like the "Feynman Point" (six 9's in a row at the 762nd digit position).

Leave comments with your phone's Pi calculation time on the AGM+FFT formula for any of the following:
   1 million, 8 million, 16 million, 130 million, 500 million, 1 billion digits(??)
(My slow Huawei U8100 takes 14 min 6 sec for 1 million)

Here's a brief summary of the available algorithms:
-AGM + FFT formula (Arithmetic Geometric Mean): This is one of the fastest available methods to calculate Pi, and is the default formula used by RealPi when you press "Start". It runs as native C++ code and is based on Takuya Ooura's pi_fftc6 program. For many millions of digits it can require a lot of memory, which often becomes the limiting factor in how many digits you can calculate.

-Machin's formula: This formula was discovered by John Machin in 1706. It's not nearly as fast as AGM + FFT, but shows you all the digits of Pi accumulating in real time as the calculation proceeds. Choose this formula in the settings menu and then press "Start". It's written in Java using the BigDecimal class. You should probably not ask it to compute much more than 10000 digits.

-Nth digit of Pi formula by Gourdon: This formula shows that it's possible, surprisingly, to calculate decimal digits of Pi "in the middle" without calculating the preceding digits. When you press the "Nth Digit" button RealPi determines 9 digits of Pi ending with the digit position you specify. It runs as native C++ code and is based on Xavier Gourdon's pidec program. Although it's faster than Machin's formula it can't beat the AGM + FFT formula in speed, however it takes almost no memory.

-Nth digit of Pi formula by Bellard: Gourdon's algorithm for the Nth digit of Pi can't be used for the first 50 digits, so this formula by Fabrice Bellard is selected automatically when the requested digit position is small.

Search function:
Use this to find patterns in the digits of Pi such as your birthday. For best results calculate at least one million digits of Pi using the AGM + FFT formula, then select the "Search for Patterns" menu option. If the search menu option is greyed out then you haven't performed a Pi calculation by pressing the Start button.

For accurate benchmark timing ensure that no other applications are running. Note that the AGM+FFT algorithm works in powers of 2, so calculating 10 million digits takes just as much time and memory as calculating 16 million digits. The benchmark sizes above take this into account.

Permissions:
This application is capable of running while your device is in sleep mode, but it won't do so unless you enable the "Calculate when in sleep" settings option. When calculating many digits of Pi you should enable this option. While not calculating Pi or after the calculation finishes your device will go into deep sleep as usual.

Warnings:
This app can drain your battery quickly while calculating, especially if the "Calculate when in sleep" option is selected. You might want to connect your charger.

Calculation speed depends on your device's CPU speed, memory, and whether it has hardware floating point support.

At very large numbers of digits RealPi may terminate unexpectedly or not produce an answer. It could also take a very long time to run (years). This is due to the large amount of memory and CPU time needed. The upper limit on the number of digits you can calculate depends on your mobile device.

Changes to the "Calculate when in sleep" option take effect for the next Pi calculation, not in the middle of a calculation, so set it before you start.