Arithmetic-geometric mean/Calculate Pi: Difference between revisions

=={{header|Nim}}==

<lang Nim>from math import sqrt

import times

import bignum

#---------------------------------------------------------------------------------------------------

func sqrt(value, guess: Int): Int =

result = guess

while true:

let term = value div result

if abs(term - result) <= 1:

break

result = (result + term) shr 1

#---------------------------------------------------------------------------------------------------

func isr(term, guess: Int): Int =

var term = term

result = guess

let value = term * result

while true:

if abs(term - result) <= 1:

break

result = (result + term) shr 1

term = value div result

#---------------------------------------------------------------------------------------------------

func calcAGM(lam, gm: Int; z: var Int; ep: Int): Int =

var am: Int

var lam = lam

var gm = gm

var n = 1

while true:

am = (lam + gm) shr 1

gm = isr(lam, gm)

let v = am - lam

let zi = v * v * n

if zi < ep:

break

dec z, zi

inc n, n

lam = am

result = am

#---------------------------------------------------------------------------------------------------

func bip(exp: int; man = 1): Int {.inline.} = man * pow(10, culong(exp))

#---------------------------------------------------------------------------------------------------

func compress(str: string; size: int): string =

if str.len <= 2 * size: str

else: str[0..<size] & "..." & str[^size..^1]

#———————————————————————————————————————————————————————————————————————————————————————————————————

import os

import parseutils

import strutils

const DefaultDigits = 25_000

var d = DefaultDigits

if paramCount() > 0:

if paramStr(1).parseInt(d) > 0:

if d notin 1..999_999:

d = DefaultDigits

let t0 = getTime()

let am = bip(d)

let gm = sqrt(bip(d + d - 1, 5), bip(d - 15, int(sqrt(0.5) * 1e15)))

var z = bip(d + d - 2, 25)

let agm = calcAGM(am, gm, z, bip(d + 1))

let pi = agm * agm * bip(d - 2) div z

var piStr = $pi

piStr.insert(".", 1)

let dt = (getTime() - t0).inMicroseconds.float

let timestr = if dt > 1_000_000:

(dt / 1e6).formatFloat(ffDecimal, 2) & " s"

elif dt > 1000:

$(dt / 1e3).toInt & " ms"

else:

$dt.toInt & " µs"

echo "Computed ", d, " digits in ", timeStr

echo "π = ", compress(piStr, 20), "..."</lang>

{{out}}

<pre>Computed 25000 digits in 72 ms

π = 3.141592653589793238...81377399510065895288...</pre>