Real Pi Benchmark 2.2

RealPi offers a selection of advanced Pi calculation algorithms that are among the most sophisticated available. This application functions as a standard for evaluating the CPU and memory performance of your Android device. It allows you to compute the value of Pi to a precision level determined by you. By analyzing the resulting digits, you can search for specific patterns such as identifying your birthday within Pi or locating renowned sequences like the "Feynman Point," which consists of six consecutive 9s at the 762nd digit. There is no fixed limit on the number of decimals you can calculate; if you encounter any issues, refer to the "Warnings" section below.

Feel free to share your computation time using the AGM+FFT formula for 1 million digits along with the maximum number of digits you were able to calculate, assessing your phone's memory capabilities. The developer's Nexus 6p, for instance, processed 1 million digits in 5.7 seconds using this formula. It's important to note that the AGM+FFT algorithm operates in powers of 2, meaning that computing 10 million digits consumes equivalent time and memory as calculating 16 million digits (the internal precision is detailed in the output). On devices with multi-core processors, RealPi assesses the efficiency of a single core. For precise benchmark results, ensure that no other applications are active and that your device is not operating at a temperature that might restrict CPU performance.

Functionality Overview:

• Search Function: Utilize this feature to identify patterns in Pi, such as significant dates like your birthday. For optimal outcomes, compute a minimum of one million digits employing the AGM+FFT formula before selecting the "Search for Patterns" from the menu.

The following algorithms are available:

• AGM + FFT Formula (Arithmetic Geometric Mean): One of the quickest methods for computing Pi, utilized by default when initiating a calculation in RealPi. This algorithm runs as native C++ code and is based on Takuya Ooura's pi_fftc6 program. However, calculating numerous digits may necessitate substantial memory resources, often impacting the total digit count achievable.
• Machin's Formula: Developed by John Machin in 1706, this formula reveals all Pi digits steadily as the computation progresses, though it's not as rapid as AGM + FFT. By selecting this formula in the settings and commencing the calculation, users can view all Pi digits accumulating in real-time. Written in Java utilizing the BigDecimal class, long calculation times may commence around 200,000 digits; nevertheless, with modern devices, one million digits can be computed and displayed using Machin's method with patience.
• Nth Digit of Pi Formula by Gourdon: Demonstrating an unconventional approach by calculating Pi decimals midway without determining prior digits, this formula operates efficiently with minimal memory usage. Activating this formula in RealPi allows for uncovering nine specified Pi digits concluding with the designated position. With native C++ code running based on Xavier Gourdon's pidec program, it surpasses Machin's method in speed but falls short compared to AGM + FFT.
• Nth Digit of Pi Formula by Bellard: To compute initial Pi digits (less than 50), Bellard's approach supersedes Gourdon's technique limiting the Nth digit calculation for such initial cases.

• Additional Options: Enabling the "Calculate when in sleep" feature permits RealPi to operate even when your screen is off, particularly beneficial during extended Pi calculations. Subsequently or post-calculation completion, your device resumes deep sleep mode conventionally.

• Warnings:
• This application can swiftly deplete your battery during prolonged computations, particularly if "Calculate when in sleep" is activated.
• The speed of calculations is contingent upon your device's CPU and memory capacities. RealPi may terminate unexpectedly or produce no result when processing large digit quantities; such scenarios could additionally result from extensive CPU processing time or memory requirements. The maximum number of digits calculable is dictated by your Android device specifications.

Modifications to the "Calculate when in sleep" setting take effect upon initiating subsequent Pi computations rather than midway through a calculation process.