pi

Documentation

Overview

Package pi calculates the nth and 8 following fractional decimal digits of pi using a Bailey-Borwein-Plouffe algorithm (see https://wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula). This allows any arbitrary fractional digit of pi to be calculated independently of the preceding digits albeit with longer calculation times as the value of n increases because of the need to calculate prime numbers of increasing value.

NOTE 1: This package is intended to be used in distributed computing and cloud scaling demos, and does not guarantee accuracy or efficiency of calculated fractional digits.

NOTE 2: The algorithms used invMod, powMod, and BPPDigits are based on the work of Fabrice Bellard (original source code published at https://bellard.org/pi/pi.c).

Example

package main

import (
	"fmt"
	"log"
	"os"

	"github.com/go-logr/stdr"
	pi "github.com/memes/pi/v2"
)

func main() {
	// Enable verbose library logging to standard library logger via go-logr/stdr
	_ = stdr.SetVerbosity(1)
	pi.Logger = stdr.New(log.New(os.Stdout, "", log.Lshortfile))
	// Calculate the first 9 decimal digits of pi
	digits := pi.BBPDigits(0)
	fmt.Printf("The first 10 digits of pi are: 3.%s\n", digits)
}

Output:

pi.go:110: "level"=1 "msg"="BBPDigits: enter" "n"=0
pi.go:172: "level"=1 "msg"="BBPDigits: exit" "n"=0 "result"="141592653"
The first 10 digits of pi are: 3.141592653

Index

• Variables
• func BBPDigits(n uint64) string
• func FindNextPrime(n int64) int64

Examples

• Package
• BBPDigits
• FindNextPrime

Variables

var (
	// The package logr.Logger instance to use.
	//nolint: gochecknoglobals // Allow package consumers to set the logger
	Logger = logr.Discard()
	// The number of Miller-Rabin rounds to use in FindNextPrime when
	// determining if an integer is probabilistically a prime. A value of
	// zero will apply a Baillie-PSW only test and requires Go 1.8+.
	//nolint: gochecknoglobals // Allow package consumers to override
	MillerRabinRounds = 0
)

Functions

func BBPDigits

func BBPDigits(n uint64) string

Implements a BBP spigot algorithm to determine the nth and 8 following fractional decimal digits of pi at the specified zero-based offset.

Example

package main

import (
	"fmt"

	pi "github.com/memes/pi/v2"
)

func main() {
	// Print the first 100 digits of pi using a default calculator
	fmt.Printf("The first 100 digits of pi are: 3.")
	for n := uint64(0); n < 99; n += 9 {
		fmt.Print(pi.BBPDigits(n))
	}
	fmt.Println()
}

Output:

The first 100 digits of pi are: 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067

func FindNextPrime

func FindNextPrime(n int64) int64

Return the next largest prime number that is greater than n.

Example

package main

import (
	"fmt"

	pi "github.com/memes/pi/v2"
)

func main() {
	// Find the first prime number after 10,000
	nextPrime := pi.FindNextPrime(10000)
	fmt.Printf("The first prime number greater than 10000 is %d\n", nextPrime)
}

Output:

The first prime number greater than 10000 is 10007